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# There are 15 students in a group. 10 students of this group

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Intern
Joined: 22 Oct 2007
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There are 15 students in a group. 10 students of this group [#permalink]

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22 Oct 2007, 10:18
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Question Stats:

100% (01:01) correct 0% (00:00) wrong based on 1 sessions

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There are 15 students in a group. 10 students of this group are boys.
5 students were invited to an interview. What is a probability that 3 of them will be girls?
Director
Joined: 11 Jun 2007
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22 Oct 2007, 10:59
Summerfish wrote:
There are 15 students in a group. 10 students of this group are boys.
5 students were invited to an interview. What is a probability that 3 of them will be girls?

prob that 3 will be girls from group of 5 = 5C3 =
5*4*3*2*1 / 3*2*1 = 20

total probability = 15C5 = 15! / 5! 10!
15*14*13*12*11 / 5*4*3*2*1 = 7*13*3*11 = 3003

so 20/3003
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22 Oct 2007, 11:05
Summerfish wrote:
There are 15 students in a group. 10 students of this group are boys.
5 students were invited to an interview. What is a probability that 3 of them will be girls?

Method (I)

10 Boys 5 Girls

Prob( 3 Girls and 2 Boys) = (5C3)x(5/15)(4/14)(3/13)(10/12)(9/11)
= 150/1001

Method (II)

Prob(3 Girls and 2 Boys) = (5C3)x(10C2)/(15C5)
= 150/1001
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22 Oct 2007, 20:35
So, what is the right answer - 150/1001 or 20/3003 ?

When I counted - I got probability 1/9.

But I think that it is more likely to be 150/1001.
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23 Oct 2007, 06:27
Manager
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24 Oct 2007, 12:02
150/1001

Total outcomes n(S) = 15C5 = 3003
3 girls will be selected which means 3 girls out of 5 and 2 boys out of 10 are selected,
so n(E) = 5C3.10C2 = 450

P = n(E)/N(S) = 450/3003 = 150/1001
24 Oct 2007, 12:02
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