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# A team of 6 cooks is chosen from 8 men and 5 women. The team

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A team of 6 cooks is chosen from 8 men and 5 women. The team [#permalink]

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16 Nov 2012, 06:38
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A team of 6 cooks is chosen from 8 men and 5 women. The team must have at least 2 men and at least 3 women. How many ways can this team be created?

A) 140
B) 320
C) 560
D) 700
E) 840

For those of you studying Combinations and Probability, we've posted a free lesson on combinations here:

http://www.gmatpill.com/gmat-practice-t ... ons-lesson

The video explanation for the above question is at 22:13

Part 1: Combination Framework - Dice, Marbles, Pocket Pair"
Part 2: Apply to GMAT - Word Problems
Part 3: Poker Probability - Pocket Pair vs Pocket Aces, Flush/Full House
00:00 - Intro
01:00 - Warmup
02:12 - Part 1 Overview: Combinations & Permutations vs Variations
08:35 - Part 1 Details: Picking Teams, Dice, Pocket Pair, Dating
17:21 - Part 2: Apply to GMAT - Word Problem #1
22:13 - Part 2: Apply to GMAT - Word Problem #2
31:34 - Part 2: Apply to GMAT - Word Problem #3
38:04 - Part 3: Poker Probability - Pocket Pair vs Pocket Aces
43:40 - Part 3: Poker Probability - Given Pocket Aces, 3-of-a-Kind?
46:13 - Part 3: Poker Probability - 1-Pair by 5th Flop
49:59 - Part 3: Poker Probability - Full House/Flush
1:00:00 - Conclusion
[Reveal] Spoiler: OA
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16 Nov 2012, 07:14
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gmatpill wrote:
A team of 6 cooks is chosen from 8 men and 5 women. The team must have at least 2 men and at least 3 women. How many ways can this team be created?

A) 140
B) 320
C) 560
D) 700
E) 840

Only possible combinations are a team of 2M, 4 W or 3M,3W.

Possible ways to make a team of 2M,4W = 8C2 * 5C4 =28*5 =140
Possible ways to make a team of 3M,3W = 8C3* 5C3 = 56*10 = 560

Total possible ways = 140+560 = 700

Ans D it is.
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24 Dec 2012, 01:32
Could someone point out where my thought process is faltering.

I did
$$8C2 * 5C3 * 8C1$$

8C1 - after choosing 2 men and and 3 women it doesn't matter who you pick from the remaining 8, so $$8C1$$

Await valued response.
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24 Dec 2012, 01:49
eaakbari wrote:
Could someone point out where my thought process is faltering.

I did
$$8C2 * 5C3 * 8C1$$

8C1 - after choosing 2 men and and 3 women it doesn't matter who you pick from the remaining 8, so $$8C1$$

Await valued response.

This way you are counting some teams more than once.

Consider that you get A and B (men) from 8C2, X, Y, Z (women) from 5C3 and C (man) from 8C1, so your group is {A, B, C, X, Y, Z}.

But if you get A and C (men) from 8C2, X, Y, Z (women) from 5C3 and B (man) from 8C1, your group will still be {A, B, C, X, Y, Z}.

Hope it's clear.
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24 Dec 2012, 02:02
Bunuel wrote:
eaakbari wrote:
Could someone point out where my thought process is faltering.

I did
$$8C2 * 5C3 * 8C1$$

8C1 - after choosing 2 men and and 3 women it doesn't matter who you pick from the remaining 8, so $$8C1$$

Await valued response.

This way you are counting some teams more than once.

Consider that you get A and B (men) from 8C2, X, Y, Z (women) from 5C3 and C (man) from 8C1, so your group is {A, B, C, X, Y, Z}.

But if you get A and C (men) from 8C2, X, Y, Z (women) from 5C3 and B (man) from 8C1, your group will still be {A, B, C, X, Y, Z}.

Hope it's clear.

Ahhh, yes. I do understand now.

Thanks, Bunuel, for the wonderful explanation.
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Re: A team of 6 cooks is chosen from 8 men and 5 women. The team [#permalink]

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25 Dec 2012, 20:08
OA: D-700.

GMATPill/Bunuel,
Is it really a 700+ level Q ? It's pretty easy guys...!

In that case combinations going to be an easy topic in GMAT..
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Re: A team of 6 cooks is chosen from 8 men and 5 women. The team [#permalink]

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26 Dec 2012, 02:26
debayan222 wrote:
OA: D-700.

GMATPill/Bunuel,
Is it really a 700+ level Q ? It's pretty easy guys...!

In that case combinations going to be an easy topic in GMAT..

GMAT combination/probability questions are fairly straightforward, so you won't see much harder questions on these topics on the exam.
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Re: A team of 6 cooks is chosen from 8 men and 5 women. The team [#permalink]

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26 Dec 2012, 04:22
Bunuel wrote:
debayan222 wrote:
OA: D-700.

GMATPill/Bunuel,
Is it really a 700+ level Q ? It's pretty easy guys...!

In that case combinations going to be an easy topic in GMAT..

GMAT combination/probability questions are fairly straightforward, so you won't see much harder questions on these topics on the exam.

Great to know that Bunuel...!
Well, in that case Qs. in your signature and those in the GMAT Club tests (obviously apart from OG Qs.) would be suffice for 700+ in GMAT I think as far as combination/probability questions are concerned...!

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Re: A team of 6 cooks is chosen from 8 men and 5 women. The team [#permalink]

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27 Dec 2012, 21:56
gmatpill wrote:
A team of 6 cooks is chosen from 8 men and 5 women. The team must have at least 2 men and at least 3 women. How many ways can this team be created?

A) 140
B) 320
C) 560
D) 700
E) 840

M M W W W M/W

This means we could have either combinations:
(1) 2MEN 4WOMEN
(2) 3MEN 3WOMEN

We will add the total number of both possibilities:
8!/6!2! * 5!/4!1! + 8!/3!5! * 5!/3!2! = 140 + 560 = 700

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A team of 6 cooks is chosen from 8 Men and 5 Women [#permalink]

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01 Sep 2013, 18:06
A team of 6 cooks is chosen from 8 Men and 5 Women. The team must have at least 2 men and at least 3 woen. How many ways can we form this team?

A) 140
B) 320
C) 560
D) 700
E) 840

Solution: We have two possibilities 2M 4F or 3M 3F
(8C2)(5C3)+(8C3)(5C3)=700

I am trying another method but I am not getting it correctly. So for The first scenario 1) 3M 4F
MMFFFF
We can use a permutation approach. For the first man we have 8 choices. Second man 7. Likewise for the females. 5 for the first....2 for the last. We get
(8*7)*(5*4*3*2)
Now here is what is confusing me. Since I have MMFFFF and order doesn't matter the number of ways to arrange 3M's & 4F's is 6!/(2!*4!). I know I have to divide by 2! and 4! because we have duplicates and order doesn't matter but what about the 6!??? Should we include or exclude it? The answer has it excluded, but why?? I feel without the 6! we don't take into account MFFFMF or FFMFMF.... etc. What am I doing wrong?
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Re: A team of 6 cooks is chosen from 8 Men and 5 Women [#permalink]

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28 Sep 2013, 01:11
(8C2)(5C3)+(8C3)(5C3)=28*10 + 56*10 = 280 + 560 = 840 --> E

are you sure its D? Please explain
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Re: A team of 6 cooks is chosen from 8 Men and 5 Women [#permalink]

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28 Sep 2013, 01:54
alphabeta1234 wrote:
A team of 6 cooks is chosen from 8 Men and 5 Women. The team must have at least 2 men and at least 3 woen. How many ways can we form this team?

A) 140
B) 320
C) 560
D) 700
E) 840

Solution: We have two possibilities 2M 4F or 3M 3F
(8C2)(5C3)+(8C3)(5C3)=700

I am trying another method but I am not getting it correctly. So for The first scenario 1) 3M 4F
MMFFFF
We can use a permutation approach. For the first man we have 8 choices. Second man 7. Likewise for the females. 5 for the first....2 for the last. We get
(8*7)*(5*4*3*2)
Now here is what is confusing me. Since I have MMFFFF and order doesn't matter the number of ways to arrange 3M's & 4F's is 6!/(2!*4!). I know I have to divide by 2! and 4! because we have duplicates and order doesn't matter but what about the 6!??? Should we include or exclude it? The answer has it excluded, but why?? I feel without the 6! we don't take into account MFFFMF or FFMFMF.... etc. What am I doing wrong?

Hi,

You are only finding the different combinations and not concerned about the ordering of the combinations. Suppose the females are f1, f2, f3 , f4 and f5, including f1 and f2 means you do not have to consider f1, f2 and f2, f1 as separate. You do it only once. Hence you have to use the combination formula.
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A team of 6 cooks is chosen from 8 men and 5 women. The team [#permalink]

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01 Oct 2013, 11:52
Hi,

I have the GMAT coming up on November 7th. I'm starting to panic because I get almost every PS problem that involves probabilities & selection wrong.

By selection I mean problems like this:

A team of 6 cooks is chosen from 8 men and 5 women. The team must have at least 2 men and at least 3 women. How many ways can this team be created?

A) 140
B) 320
C) 560
D) 700
E) 840

It's not that I don't get the formulas, I do. I just have no idea when to apply which formula. Or how you guys/ladies are looking at a problem and thinking "oh if I break this problem down into simpler terms, I can use formula ABC to solve it". It's exceedingly frustrating, because I'm getting about 90% of the problems incorrect. I just don't know what to do. I'm usually pretty good at math, I took the GRE about 7 years ago and was around 760 on the math section, but the GMAT questions just seem so different.

Last edited by Narenn on 01 Oct 2013, 20:24, edited 2 times in total.
Topic Moved. Always post the topic in relevant forum
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Re: No idea how to apply the PS formulae I'm learning here [#permalink]

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01 Oct 2013, 12:37
AccipiterQ wrote:
Hi,

I have the GMAT coming up on November 7th. I'm starting to panic because I get almost every PS problem that involves probabilities & selection wrong.

By selection I mean problems like this:

A team of 6 cooks is chosen from 8 men and 5 women. The team must have at least 2 men and at least 3 women. How many ways can this team be created?

A) 140
B) 320
C) 560
D) 700
E) 840

It's not that I don't get the formulas, I do. I just have no idea when to apply which formula. Or how you guys/ladies are looking at a problem and thinking "oh if I break this problem down into simpler terms, I can use formula ABC to solve it". It's exceedingly frustrating, because I'm getting about 90% of the problems incorrect. I just don't know what to do. I'm usually pretty good at math, I took the GRE about 7 years ago and was around 760 on the math section, but the GMAT questions just seem so different.

Question is not so difficult. Only thing matters is how do we simplify the information.

We know the team must have AT-LEAST 2 men and AT-LEAST 3 women. So the possible combinations are 2(M) and 4(W) or 3(M) and 3(W)

Case I :- 2 Men and 4 Women -------> selection of 2 men from 8 men AND selection of 4 women from 5 women ------> 8 C 2 * 5 C 4 -------> 28*5 -----> 140 teams

Case II :- 3 Men and 3 Women -------> selection of 3 men from 8 men AND selection of 3 women from 5 women ------> 8 C 3 * 5 C 3 -------> 56*10 -----> 560 teams

Total Number of teams = 140 + 560 = 700 ---------> Choice D

Hope that Helps!

PS :- For reference check my Permutations and Combinations article listed in my signature.
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Re: No idea how to apply the PS formulae I'm learning here [#permalink]

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01 Oct 2013, 12:39
Narenn wrote:
AccipiterQ wrote:
Hi,

I have the GMAT coming up on November 7th. I'm starting to panic because I get almost every PS problem that involves probabilities & selection wrong.

By selection I mean problems like this:

A team of 6 cooks is chosen from 8 men and 5 women. The team must have at least 2 men and at least 3 women. How many ways can this team be created?

A) 140
B) 320
C) 560
D) 700
E) 840

It's not that I don't get the formulas, I do. I just have no idea when to apply which formula. Or how you guys/ladies are looking at a problem and thinking "oh if I break this problem down into simpler terms, I can use formula ABC to solve it". It's exceedingly frustrating, because I'm getting about 90% of the problems incorrect. I just don't know what to do. I'm usually pretty good at math, I took the GRE about 7 years ago and was around 760 on the math section, but the GMAT questions just seem so different.

Question is not so difficult. Only thing matters is how do we simplify the information.

We know the team must have AT-LEAST 2 men and AT-LEAST 3 women. So the possible combinations are 2(M) and 4(W) or 3(M) and 3(W)

Case I :- 2 Men and 4 Women -------> selection of 2 men from 8 men AND selection of 4 women from 5 women ------> 8 C 2 * 5 C 4 -------> 28*5 -----> 140 teams

Case II :- 3 Men and 3 Women -------> selection of 3 men from 8 men AND selection of 3 women from 5 women ------> 8 C 3 * 5 C 3 -------> 56*10 -----> 560 teams

Total Number of teams = 140 + 560 = 700 ---------> Choice D

Hope that Helps!

Thanks for the reply; it's actually a question posted here elsewhere, I just was using it as a sample of the type of problem. The issue I have is that I have no idea how to apply these formulae or when to apply them.
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Re: No idea how to apply the PS formulae I'm learning here [#permalink]

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01 Oct 2013, 12:47
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AccipiterQ wrote:
Thanks for the reply; it's actually a question posted here elsewhere, I just was using it as a sample of the type of problem. The issue I have is that I have no idea how to apply these formulae or when to apply them.

Ok. Refer the Article 'Permutations and Combinations' listed in my Signature below. I am sure it will help you understand when to apply which formula.

Thanks

Narenn
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Re: No idea how to apply the PS formulae I'm learning here [#permalink]

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01 Oct 2013, 16:51
Narenn wrote:
AccipiterQ wrote:
Thanks for the reply; it's actually a question posted here elsewhere, I just was using it as a sample of the type of problem. The issue I have is that I have no idea how to apply these formulae or when to apply them.

Ok. Refer the Article 'Permutations and Combinations' listed in my Signature below. I am sure it will help you understand when to apply which formula.

Thanks

Narenn

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Re: A team of 6 cooks is chosen from 8 men and 5 women. The team [#permalink]

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02 Oct 2013, 02:38
AccipiterQ wrote:
Hi,

I have the GMAT coming up on November 7th. I'm starting to panic because I get almost every PS problem that involves probabilities & selection wrong.

By selection I mean problems like this:

A team of 6 cooks is chosen from 8 men and 5 women. The team must have at least 2 men and at least 3 women. How many ways can this team be created?

A) 140
B) 320
C) 560
D) 700
E) 840

It's not that I don't get the formulas, I do. I just have no idea when to apply which formula. Or how you guys/ladies are looking at a problem and thinking "oh if I break this problem down into simpler terms, I can use formula ABC to solve it". It's exceedingly frustrating, because I'm getting about 90% of the problems incorrect. I just don't know what to do. I'm usually pretty good at math, I took the GRE about 7 years ago and was around 760 on the math section, but the GMAT questions just seem so different.

Merging similar topics. Please refer to the solutions above.
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Re: A team of 6 cooks is chosen from 8 men and 5 women. The team [#permalink]

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15 Jan 2016, 13:31
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Re: A team of 6 cooks is chosen from 8 men and 5 women. The team   [#permalink] 15 Jan 2016, 13:31
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