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# From a group of 6 boys and 6 girls a volleyball team of 6 players

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Manager
Joined: 02 Mar 2018
Posts: 65
Location: India
GMAT 1: 640 Q51 V26
GPA: 3.1
From a group of 6 boys and 6 girls a volleyball team of 6 players  [#permalink]

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Updated on: 05 Aug 2018, 10:23
3
00:00

Difficulty:

55% (hard)

Question Stats:

64% (02:57) correct 36% (02:53) wrong based on 61 sessions

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From a group of 6 boys and 6 girls a volleyball team of 6 players is to be selected. What is the probability that the team consists of 4 boys and 2 girls?

A) $$\frac{5}{33}$$

B) $$\frac{225}{308}$$

C) $$\frac{5}{22}$$

D) $$\frac{225}{311}$$

E) $$\frac{75}{308}$$

Originally posted by gsingh0711 on 05 Aug 2018, 09:53.
Last edited by generis on 05 Aug 2018, 10:23, edited 1 time in total.
Edited and formatted the question, renamed the topic
Manager
Joined: 02 Mar 2018
Posts: 65
Location: India
GMAT 1: 640 Q51 V26
GPA: 3.1
Re: From a group of 6 boys and 6 girls a volleyball team of 6 players  [#permalink]

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05 Aug 2018, 09:54
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1
Explanation:

Total number of outcomes is selection of 6 players out of 12 = 12C6 = 924
Favorable number of ways is selection of 4 boys and 2 girls = 6C4 × 6C2 = 15 × 15 = 225 ways

⇒ Required probability = favorable outcomes / total outcomes = 225/924 = 75/308

I think, I deserve a kudus LOL
Intern
Joined: 21 Aug 2018
Posts: 1
Re: From a group of 6 boys and 6 girls a volleyball team of 6 players  [#permalink]

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21 Aug 2018, 13:10
Explanation with less math (if you simplify):

probability of choosing 4 boys (out of 6) out of 12 people: 6/12 * 5/11 * 4/10 * 3/9
probability of choosing 2 girls (out of 6) out of 8 people: 6/8 * 5/7
the order doesn’t matter between the 6, discounting changing girls/boys between themselves : *6! / 4!2!

multiply those to get the answer
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Re: From a group of 6 boys and 6 girls a volleyball team of 6 players  [#permalink]

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23 Aug 2018, 17:02
gsingh0711 wrote:
From a group of 6 boys and 6 girls a volleyball team of 6 players is to be selected. What is the probability that the team consists of 4 boys and 2 girls?

A) $$\frac{5}{33}$$

B) $$\frac{225}{308}$$

C) $$\frac{5}{22}$$

D) $$\frac{225}{311}$$

E) $$\frac{75}{308}$$

The number of ways to select the 4 boys for the team is 6C4:

(6 x 5 x 4 x 3)/4! = (6 x 5 x 4 x 3)/(4 x 3 x 2) = 15

The number of ways to select the 2 girls for the team is 6C2:

(6 x 5)/2! = 15

The number of ways to select 6 people out of the group of 12 is 12C6:

(12 x 11 x 10 x 9 x 8 x 7)/6! = (12 x 11 x 10 x 9 x 8 x 7)/(6 x 5 x 4 x 3 x 2) = 11 x 2 x 3 x 2 x 7 = 924

So the probability of selecting 4 boys and 2 girls for the team is (15 x 15)/924 = 225/924 = 75/308.

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Re: From a group of 6 boys and 6 girls a volleyball team of 6 players   [#permalink] 23 Aug 2018, 17:02
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