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

Question

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

Vips0000 · Accepted Answer

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.

eaakbari · Answer

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.

Bunuel · Answer

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.

eaakbari · Answer

Ahhh, yes. I do understand now.

Thanks, Bunuel, for the wonderful explanation.

bagdbmba · Answer

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..

Bunuel · Answer

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

bagdbmba · Answer

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...! Appreciate your thoughts on this...

mbaiseasy · Answer

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

Answer: D

alphabeta1234 · Answer

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?

dobler · Answer

(8C2)(5C3)+(8C3)(5C3)=28*10 + 56*10 = 280 + 560 = 840 --> E

are you sure its D? Please explain

SVaidyaraman · Answer

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.

AccipiterQ · Answer

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.

Narenn · Answer

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.

AccipiterQ · Answer

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.

Narenn · Answer

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

AccipiterQ · Answer

I just downloaded several of your PDFs, looks like I have some more study material! Thanks!

luisdicampo · Answer

Deconstructing the Question  
We form a team of  6  cooks from  8 men  and  5 women .
The team must have  at least 2 men  and  at least 3 women .

Possible (men, women) splits for a 6-person team that satisfy both constraints:
 (2,4)\ 	ext{and}\ (3,3)

Step-by-step  
 Case 1: 2 men and 4 women 
 C(8,2)\cdot C(5,4)=28\cdot 5=140

Case 2: 3 men and 3 women 
 C(8,3)\cdot C(5,3)=56\cdot 10=560

Total 
 140+560=700

Answer:     (D) 700

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

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