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A class is made up of 9 seniors and 7 juniors. You select 3

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gamjatang
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A class is made up of 9 seniors and 7 juniors. You select 3 [#permalink] New post   24 Nov 2005, 05:44
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A class is made up of 9 seniors and 7 juniors.
You select 3 of them and make a committee.
In how many cases can you make a committee with at least one senior and at least one junior?



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Re: A class is made up of 9 seniors and 7 juniors. You select 3 [#permalink] New post   24 Nov 2005, 07:13
gamjatang wrote:
A class is made up of 9 seniors and 7 juniors.
You select 3 of them and make a committee.
In how many cases can you make a committee with at least one senior and at least one junior?


At least translates into two possibilities:

1. One senior and two juniors <or> 2.Two seniors and one junior

Since order doesn`t matter, this is a combinations problem.

<or> = addition (+)

1. 9C1*7C2=189
2. 9C2*7C1=252

252+189= 441
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Re: A class is made up of 9 seniors and 7 juniors. You select 3 [#permalink] New post   24 Nov 2005, 08:23
The outcome can be

(2 seniors and 1 junior) OR (2 juniors and 1 senior)
( C(9,2) * C(7,1) ) + ( C(7,2) * C(9,1) )
= 441
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Re: A class is made up of 9 seniors and 7 juniors. You select 3 [#permalink] New post   24 Nov 2005, 09:37
3 member combinations are: (1S+2J)+(2S+1J)
so the committee= (9C1x7C2)+(9C2x7C1) = (9x21)+(36x7)=441
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Re: A class is made up of 9 seniors and 7 juniors. You select 3 [#permalink] New post   24 Nov 2005, 14:37
441...different approach...total combinations are 16c3=56. ttl comb of no seniors is 9c3. ttl comb of no juniors is 7c3. 16c3-9c3-7c3=441
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Re: A class is made up of 9 seniors and 7 juniors. You select 3 [#permalink] New post   24 Nov 2005, 17:32
Thanks for the explanation, everyone.

The OA is indeed 441.

However, I still don't understand why I am wrong.

The following is my work, and I hope someone will find what I did wrong here.

*****************************************

Cases of picking ONE student from senior group = 9
Cases of picking ONE student from junior group = 7

After picking 2 students from the class, there are total of 14 students left.

Cases of picking ANY ONE student from the students left = 14

Therefore, 9 * 7 * 14 = 882.

What did I do wrong here ?? Someone tell me, please...



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Re: A class is made up of 9 seniors and 7 juniors. You select 3 [#permalink]
24 Nov 2005, 17:32
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