A project manager needs to select a group of 4 people from a total of

Question

A project manager needs to select a group of 4 people from a total of 4 men and 4 women. How many possible group combinations exist such that no group has all men or all women?

A) 72
B) 68
C) 74
D) 82
E) 48

Source: Platinum GMAT 
 Kudos for a correct  solution .

reto · Answer

First list all the possible combinations of Groups wit F = Female and M = Male:

MMMF
Total Combinations of 16 (4*3*2/3! *4)

FFFM
Total Combinations of 16 (same as above)

FFMM
Total Combinations of 36 (4*3/2! * 4*3/2!)

Alltogether that makes 68.

Answer Choice B

GMATinsight · Answer

Total Ways of Selecting 4 members randomly out of 8 = 8 C 4 = 70

Total Ways of Selecting 4 members out of 4 Men = 4 C 4 = 1

Total Ways of Selecting 4 members out of 4 Women = 4 C 4 = 1

Total Favorable cases such that all selected members are not all Men or all Women =  8 C 4  -  4 C 4  -  4 C 4  =  70  -  1  -  1  = 68

Answer: Option B

KS15 · Answer

A project manager needs to select a group of 4 people from a total of 4 men and 4 women. How many possible group combinations exist such that no group has all men or all women?

A) 72
B) 68
C) 74
D) 82
E) 48

Total No of Ways of Selecting 4 members out of 8 = 8C4 = 70
Total no of Ways of Selecting 4 members out of 4 Men = 4C4 = 1
Total Ways of Selecting 4 members out of 4 Women = 4C4 = 1

Now, No of possible combinations=70-1-1=68

Answer B

balamoon · Answer

A project manager needs to select a group of 4 people from a total of 4 men and 4 women. How many possible group combinations exist such that no group has all men or all women?

A) 72
B) 68
C) 74
D) 82
E) 48

Solution -

1. First, we will get the combination of group has all men or all women. -> 4C4 + 4C4 = 2
2. Total possible combinations without any condition = 8C4 = 70

Total combinations in a group, which do not have all men or all women -> 70 - 2 =68.

Thanks

vishwaprakash · Answer

Total Number of combination = 8C4 = \frac{(8!)}{(4! * 4!)} = 70
4 men can be selected from 4 men in 1 way
4 women can be selected from 4 women in 1 way

Total Number of combination with Only men or only women = 1 + 1 = 2

Hence required Number of combination = 70 - 2 = 68

Option B

lipsi18 · Answer

Total ways to find 3 men (M) and 1 woman(W) = 3M1W = (4!/3!)*4 =16 =same will be for 3W1M
2W2M = (4!/2!)*(4!/2!) = 36
Total combination =3M1W+2M2W+3W1M =32+36 =68

Hence answer is B
Thanks,

Bunuel · Answer

Platinum GMAT Official Solution:

Since the order in which the group is selected does not matter, we are dealing with a combinations problem (and not a permutations problem).

The formula for combinations is:
N!/((N-K)!K!)
Where N = the total number of elements from which we will select, 8 people in this case.
Where K = the total number of elements to select, 4 people in this case.

The total number of combinations is therefore:
8!/((8-4)!4!) = 70

However, two of these combinations are not valid since they have all members of one gender.

The correct answer is 70-2 = 68

ScottTargetTestPrep · Answer

Solution:

Without any restrictions, there are 8C4 = (8 x 7 x 6 x 5) / (4 x 3 x 2) = 7 x 2 x 5 = 70 possible groups of 4 people chosen from 8 people. Since there are only 2 groups that have either all men or all women (one group is all men and the other all women), 70 - 2 = 68 groups consist of people of both sexes.

Answer: B

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