How many 4 member committee can be formed from a group of x men and y

Question

How many 4 member committee can be formed from a group of x men and y women such that 3 members are of one sex and 1 member of opposite sex

(1) There are a total of 12 men and women together in the group
(2) If the number of men was y and the number of women was x then the number of committees formed would not change

Jagmeister · Answer

I am not at all sure about my approach, but this is the only line of thought that I could come up with, looking forward to the OA and explanation.

there will be 2 valid scenarios,

Scenario 1: 3 Men and 1 Woman
Scenario 2: 3 Women and 1 Man

Therefore the total number of committees formed would be

Scenario1 + Scenario2 
 xC3* yC1 + yC3*xC1

this expands to
  *(y) +  *(x)

Statement 1: x+y = 12
substituting y= 12-x and bringing it into the brackets, the above expansion reduces to

+

Taking commons

expanding

2x^2 -24x +112]

taking 2 common and cancelling

without x we can't solve this, so statement 1 is NOT enough

Statement 2: 
if the number of men was y and the number women was x, the number of committees formed would still be the same.

This statement is redundant because

*(y) +  *(x)

The above equation is symmetrical across the + so exchanging x and y would still give us the same equation

Based on the above observations I feel that the answer should be

(E) Both Statements Together are not enough

chicmon · Answer

Hi,

I have a doubt. 
can I solve equation 1 as follows:
(12c4*4!/(3!*1!))*2

SaquibHGMATWhiz · Answer

No, you can't do that.

What you are doing here is to pick 4 people from 12 randomly.

You can't assume that you are picking only 3 men + 1 woman or 3 women + 1 man. 
You can pick other combinations as well such as all men, all women, 2 women, and 2 men subject to availability and hence this is not correct.

Since you are picking 3 women and 1 man for one scenario, you must know how many men and how many women are there which we do not know from statement 1

A.Smirnova · Answer

Hi. if we combine both st. may be we can make equation ? 
(1) gives us a number -12
(2) says if the number of men was y and the number of women was x then the number of committees formed would not change

Let say the number of men x, than the number of women 12-x
First we choose 3 men from x + 1 woman from 12-x and it is equal if we choose 3 women from 12-x + 1 man from x
3Cx + 1C12-x = 3C12-x + 1Cx
(1\11, 2\10, 3\9, 8\4, 7\5, 6\6) and if we put these numbers in equation only 6\6 will work

carbonex8010 · Answer

I am getting C. Please comment on the approach.

A: Insufficient
B:
xC3*yC1=yC3*xC1
B alone insufficient

Now, replacing y=12-x
we get:
x^2-3x+2=x^2-21x+110
x=6
So, men=6, women=6
From this we can calculate the no. of ways to form the committee.

Bunuel · Answer

We are asked to find the value of xC1 * yC3 + xC3 * yC1

(1) says that x + y = 12, which is not sufficient.
(2) says that xC1 * yC3 + xC3 * yC1 = yC1 * xC3 + yC3 * xC1, which gives 0 = 0. So this statement is completely useless.

Taken together, we have one insufficient statement and one completely useless statement.

You could easily solve this by assuming values. For example, if there are 0 men and 12 women, the answer would be 0 committees. But if there were 1 man and 11 women, the answer would be more than 0 committees, whatever that number is (it's 11C3).

bumpbot · Answer

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How many 4 member committee can be formed from a group of x men and y

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How many 4 member committee can be formed from a group of x men and y

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