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by hey_thr67 » Sun May 20, 2012 10:27 pm
A 10-member student leadership committee consists of juniors and seniors. Exactly 6 students will be selected from this group to attend a national convention. What is the probability that at least 3 seniors are selected for the committee?

1- 1/10
2- 3/10
3- 3/5
4-6/7
5-13/14
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by LalaB » Sun May 20, 2012 10:51 pm
It seems that this quesiton is incomplete.nowhere is mentioned how many seniors and juniors are in this 10 member committee
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by hey_thr67 » Sun May 20, 2012 10:59 pm
Oh my....

restating the question:

A 10-member student leadership committee consists of juniors and seniors. There are 4 junior and 6 senior students. Exactly 6 students will be selected from this group to attend a national convention. What is the probability that at least 3 seniors are selected for the committee?

1- 1/10
2- 3/10
3- 3/5
4-6/7
5-13/14
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by Anurag@Gurome » Sun May 20, 2012 11:11 pm
hey_thr67 wrote:Oh my....

restating the question:

A 10-member student leadership committee consists of juniors and seniors. There are 4 junior and 6 senior students. Exactly 6 students will be selected from this group to attend a national convention. What is the probability that at least 3 seniors are selected for the committee?

1- 1/10
2- 3/10
3- 3/5
4-6/7
5-13/14
Seniors = 6, Juniors = 4
Possible combinations are (3S, 3J), (4S, 2J), (5S, 1J), (6S, 0J)
Number of ways in which at least 3 seniors are selected for the committee = (6C3 * 4C3) + (6C4 * 4C2) + (6C5 * 4C1) + (6C6 * 4C0)
= (20 * 4) + (15 * 6) + (6 * 4) + (1)
= 195
Number of ways of choosing 6 students from 10 = 10C6 = (10 * 9 * 8 * 7)/(4 * 3 * 2) = 10 * 3 * 7 = 210
Required probability = 195/210 = [spoiler]13/14[/spoiler]

The correct answer is E.[/spoiler]
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by LalaB » Sun May 20, 2012 11:31 pm
at least 3 seniors=1 -(less than 3 seniors)

please pay attention that less than 3 seniors option is true, only if -

S S J J J J

u cant have less than that,since u have 4 Juniors at most

so 1- (6!/2!*4!)/(10!/6!*4!)=195/210=13/14
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