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

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Math Expert
Joined: 02 Sep 2009
Posts: 58434
A project manager needs to select a group of 4 people from a total of  [#permalink]

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25 Jun 2015, 04:29
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Difficulty:

25% (medium)

Question Stats:

79% (01:31) correct 21% (01:58) wrong based on 109 sessions

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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.

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Re: A project manager needs to select a group of 4 people from a total of  [#permalink]

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25 Jun 2015, 04:42
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Bunuel wrote:
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.

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.

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A project manager needs to select a group of 4 people from a total of  [#permalink]

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25 Jun 2015, 06:18
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Bunuel wrote:
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.

Total Ways of Selecting 4 members randomly out of 8 = 8C4 = 70

Total Ways of Selecting 4 members out of 4 Men = 4C4 = 1

Total Ways of Selecting 4 members out of 4 Women = 4C4 = 1

Total Favorable cases such that all selected members are not all Men or all Women = 8C4 - 4C4 - 4C4 = 70 - 1 - 1 = 68

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Re: A project manager needs to select a group of 4 people from a total of  [#permalink]

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25 Jun 2015, 06:31
[quote="Bunuel"]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

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Joined: 26 Dec 2011
Posts: 115
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Re: A project manager needs to select a group of 4 people from a total of  [#permalink]

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26 Jun 2015, 00:41
2
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
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Re: A project manager needs to select a group of 4 people from a total of  [#permalink]

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26 Jun 2015, 07:39
1
Bunuel wrote:
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.

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
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Re: A project manager needs to select a group of 4 people from a total of  [#permalink]

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26 Jun 2015, 10:05
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

Thanks,
Math Expert
Joined: 02 Sep 2009
Posts: 58434
Re: A project manager needs to select a group of 4 people from a total of  [#permalink]

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29 Jun 2015, 05:29
Bunuel wrote:
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.

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
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Re: A project manager needs to select a group of 4 people from a total of  [#permalink]

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03 Oct 2019, 04:11
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Re: A project manager needs to select a group of 4 people from a total of   [#permalink] 03 Oct 2019, 04:11
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