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# A small company employs 3 men and 5 women. If a team of 4

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Director
Joined: 10 Feb 2006
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A small company employs 3 men and 5 women. If a team of 4  [#permalink]

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22 Nov 2007, 19:46
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43
00:00

Difficulty:

45% (medium)

Question Stats:

66% (01:15) correct 34% (01:23) wrong based on 1417 sessions

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A small company employs 3 men and 5 women. If a team of 4 employees is to be randomly selected to organize the company retreat, what is the probability that the team will have exactly 2 women?

A. 1/14
B. 1/7
C. 2/7
D. 3/7
E. 1/2

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24 Apr 2011, 16:17
6
9
coldteleporter wrote:
Hi all,

SECOND METHOD:
Probability of two women -> 5/8 * 4/7.

probability of two men -> 3/6 * 2/5.

Probability: (5/8 * 4/7) * (3/6 * 2/5) = 1/14.

I know something is wrong with the second method but i can't really figure out why its flawed.

Any pointers ?? thanks

The problem here is that you are arranging the people. When you select a woman out of 8 as 5/8, you are saying that you are picking a woman first. You are arranging them in this way:
WWMM
Now, if you want to un-arrange them, multiply it by the total number of arrangements i.e. 4!/(2!*2!) (because there are 2 men and 2 women so you divide by 2!s to get the total number of arrangements)

When you do that, you get 1/14 * 4!/(2!*2!) = 3/7
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26 Aug 2008, 22:02
13
4
$$P=\frac{3C2*5C2}{8C4}$$
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##### General Discussion
Manager
Joined: 27 Oct 2008
Posts: 181

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27 Sep 2009, 23:24
A small company employs 3 men and 5 women. If a team of 4 employees is to be randomly selected to organize the company retreat, what is the probability that the team will have exactly 2 women?

1/14
1/7
2/7
3/7
1/2

Soln:
= 3C2 * 5C2/8C4
= 3/7
Intern
Joined: 06 Jul 2010
Posts: 16

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07 Jul 2010, 18:24
4
For this question answer is: 3/7

Solution:
There are 5 women and 3 men. Total number of employees are 8. So, out of 8 employees we have to select 4 employees = 8C4

Out of 8 employees, we must select exactly 2 women, this implies that we must select exactly 2 men.

(5C2 X 3C2) / 8C4

Ans: 3/7

Cheers
/Milap
Joined: 31 Dec 1969
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11 Jul 2010, 03:05
1
Ok I get it. The order is not given. its random.

So we have 4*3*2/2*2 = 6 ways to arrange wwmm

so final probability is 1/14 * 6 = 3/7
Manager
Joined: 24 Apr 2010
Posts: 56

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10 Aug 2010, 21:22
is probablity the same if
rather than "2 women" it says "jena and monica" must be in (ie 2 in particular among 4)?
bit confused in that
Manager
Joined: 20 Mar 2010
Posts: 81

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11 Aug 2010, 00:17
frank1 wrote:
is probablity the same if
rather than "2 women" it says "jena and monica" must be in (ie 2 in particular among 4)?
bit confused in that

Then there is only $$C^2_2$$ or 1 way to pick women instead of $$C^4_2$$.So probability will change.
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Manager
Joined: 09 Aug 2010
Posts: 100

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24 Mar 2011, 22:15
12
3
I used to have trouble with this but for those having trouble with probablility and combinatorics. I think you can have some help from ANAGRAM.

Example: Ways to rearrange LEVEL

5! = because we have 5 letters
2! = because we have 2 Ls
2! = because we have 2 Es

Formula is 5!/2!2! = 30

YOU CAN USE THIS WITH THE PROBLEM ABOVE.

SOLUTION:

How many ways to select 4 from 8 people?
(imagine this as rearranging YYYYNNNN) 8!/4!4! = 70

How many ways to select 2 women from 5 women?
(imagine this as rearranging YYNNN) 5!/2!3! = 10

How many ways to select 2 men from 3 men?
(imagine this as rearranging YYN) 3!/2! = 3

Probability = 3 x 10 / 70 = 3/7
Intern
Joined: 07 Aug 2009
Posts: 46

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24 Apr 2011, 15:52
Hi all,

I was working on a practice test when i saw this question. Now, the problem is; i have solved it in two ways, one way(using combinations) leads to the correct answer, the other gives me something different. i would appreciate if you could point out what im doing wrong here.

Questn
A small company employs 3 men and 5 women. If a team of 4 employees is to be randomly selected to organize the company retreat, what is the probability that the team will have exactly 2 women?

a.) 1/14
b.) 1/7
c.) 2/7
d.) 3/7
e.) 1/2

first method:
5C2 * 3C2 -> it gives combination of exactly 2 women and 2 men.
8C4 -> gives total possibilities of 4 people from 5 women and 3 men.

Probability = 5C2*3C2 / 8C4 = 3/7

SECOND METHOD:
Probability of two women -> 5/8 * 4/7.

probability of two men -> 3/6 * 2/5.

Probability: (5/8 * 4/7) * (3/6 * 2/5) = 1/14.

I know something is wrong with the second method but i can't really figure out why its flawed.

Any pointers ?? thanks
Intern
Joined: 07 Aug 2009
Posts: 46

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25 Apr 2011, 11:22
VeritasPrepKarishma wrote:
coldteleporter wrote:
Hi all,

SECOND METHOD:
Probability of two women -> 5/8 * 4/7.

Quote:
The problem here is that you are arranging the people. When you select a woman out of 8 as 5/8, you are saying that you are picking a woman first. You are arranging them in this way:
WWMM
Now, if you want to un-arrange them, multiply it by the total number of arrangements i.e. 4!/(2!*2!) (because there are 2 men and 2 women so you divide by 2!s to get the total number of arrangements)

When you do that, you get 1/14 * 4!/(2!*2!) = 3/7

Hello karishma,

From what i understand, you have added all probabilities like so:
1) WWMM
2) WMMW
3) WMWM
4) MWMW
5) MMWW
6) MWWM

...such that you do not repeat arrangements that are the same, such as W1W2 and W2W1.
... right ? Thanks
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Joined: 16 Oct 2010
Posts: 8132
Location: Pune, India

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25 Apr 2011, 11:53
1
1
Yes. What you have to do is select a group. Hence you do not have to arrange them. In your second method, you got 1/14 which is the probability of getting wwmm. Since there are other such arrangements too which are all acceptable to us e.g. Wmwm since we just need a group of 2 men and 2 women irrespective of their arrangement, we multiply 1/14 by 6 (since 6 such arrangements are possible as shown by you)
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25 Apr 2011, 13:55
VeritasPrepKarishma wrote:
Yes. What you have to do is select a group. Hence you do not have to arrange them. In your second method, you got 1/14 which is the probability of getting wwmm. Since there are other such arrangements too which are all acceptable to us e.g. Wmwm since we just need a group of 2 men and 2 women irrespective of their arrangement, we multiply 1/14 by 6 (since 6 such arrangements are possible as shown by you)

Thank you Karishma. You were very helpful.
Intern
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Posts: 10
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Concentration: Social Entrepreneurship, General Management
GMAT 1: 700 Q38 V47
GPA: 3.37
WE: Marketing (Non-Profit and Government)
Re: A small company employs 3 men and 5 women. If a team of 4  [#permalink]

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25 May 2013, 10:58
Can someone please explain to me why you can't solve this by multiplying:

5/8 * 5/8 * 3/8 * 3/8?

Is it because this method doesn't take into account different order possibilities?

In general how do you know whether to solve a probability by multiplying plain fractions like this or by using factorals (!s) ?
Math Expert
Joined: 02 Sep 2009
Posts: 47152
Re: A small company employs 3 men and 5 women. If a team of 4  [#permalink]

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25 May 2013, 11:16
dawip wrote:
Can someone please explain to me why you can't solve this by multiplying:

5/8 * 5/8 * 3/8 * 3/8?

Is it because this method doesn't take into account different order possibilities?

In general how do you know whether to solve a probability by multiplying plain fractions like this or by using factorals (!s) ?

Check here: a-small-company-employs-3-men-and-5-women-if-a-team-of-56037.html#p913073

Hope it helps.
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Joined: 15 Aug 2013
Posts: 271

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10 May 2014, 15:24
VeritasPrepKarishma wrote:
Yes. What you have to do is select a group. Hence you do not have to arrange them. In your second method, you got 1/14 which is the probability of getting wwmm. Since there are other such arrangements too which are all acceptable to us e.g. Wmwm since we just need a group of 2 men and 2 women irrespective of their arrangement, we multiply 1/14 by 6 (since 6 such arrangements are possible as shown by you)

Hi Karishma,

Very helpful answer. Maybe you could clarify something for me: When we use the combinatorics method in this problem - (2c5*2c3)/4c8 - why don't we add in the permutations part like we do for the probability method?

What I mean by that is -- If i use the probability approach (favorable outcomes/total outcomes) -- I get (5/8)(4/7)(3/6)(2/5) and then I multiply that by the permutations, which means that I multiply it 4!/2!2! -- why don't we do this last part when it comes to probability?

Thanks!
Manager
Joined: 07 Apr 2014
Posts: 119
Re: A small company employs 3 men and 5 women. If a team of 4  [#permalink]

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15 Aug 2014, 12:12
Hi,

4W- 5C4
3W, 1M - 5C3*3C1
1W,3M - 5C1*3C3

Total - 8C4

1-( 4W+3W,1M +1W,3M) / TOTAL....

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Joined: 18 Aug 2014
Posts: 325
Re: A small company employs 3 men and 5 women. If a team of 4  [#permalink]

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30 Jan 2016, 17:15
Can someone explain to me why the answer is not 1/7?

I did Desired Outcomes/Total Outcomes. Obviously total is 70 we all agree on that. We also all agree that 5 women choose 2 = 10.

However, I don't see why we then do 3 men choose 2. Why does it matter which men are chosen?

Can someone explain logically rather than mathematically?
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Re: A small company employs 3 men and 5 women. If a team of 4  [#permalink]

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30 Jan 2016, 18:54
1
redfield wrote:
Why does it matter which men are chosen?
Can someone explain logically rather than mathematically?

We need to consider which men are chosen since a committee with Ann, Bea, Joe and Ed is DIFFERENT FROM a committee with Ann, Bea, Joe and Kevin

Cheers,
Brent
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Re: A small company employs 3 men and 5 women. If a team of 4  [#permalink]

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19 Feb 2016, 09:03
A small company employs 3 men and 5 women. If a team of 4 employees is to be randomly selected to organize the company retreat, what is the probability that the team will have exactly 2 women?

5C2*3C2/8C4 = 30/70 = 3/7
Re: A small company employs 3 men and 5 women. If a team of 4 &nbs [#permalink] 19 Feb 2016, 09:03

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