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

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Joined: 02 Mar 2018
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From a group of 6 boys and 6 girls a volleyball team of 6 players  [#permalink]

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New post Updated on: 05 Aug 2018, 10:23
2
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A
B
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D
E

Difficulty:

  65% (hard)

Question Stats:

63% (02:15) correct 37% (02:24) wrong based on 54 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
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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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New post 05 Aug 2018, 09:54
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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

Answer: E.

I think, I deserve a kudus LOL
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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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New post 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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New post 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.

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