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# Permutations???

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Intern
Joined: 15 Apr 2007
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31 Aug 2008, 19:04
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

I am having problems with this question:

The US Senate consists of 100 senators, two from each state. A committee consisting of five senators is to be formed.

(a) How many different committees are possible?
(b) How many committees are possible if no state may have more than one senator on the committee?
(c) What’s the probability that no state will have both of its senators on a committee?

I think the first (a) should be: 100*99*98*97*96

But I'm not sure about (b) and (c). Help.

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SVP
Joined: 29 Aug 2007
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31 Aug 2008, 20:21
kamilaak wrote:
I am having problems with this question:

The US Senate consists of 100 senators, two from each state. A committee consisting of five senators is to be formed.

(a) How many different committees are possible?
(b) How many committees are possible if no state may have more than one senator on the committee?
(c) What’s the probability that no state will have both of its senators on a committee?

I think the first (a) should be: 100*99*98*97*96

But I'm not sure about (b) and (c). Help.

a. 100c5 = (100x99x98x97x96x95!)/(5x4x3x2x1x95!) = 5x33x49x97x96
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Current Student
Joined: 11 May 2008
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31 Aug 2008, 20:36
well, let me try my luck..

2)if no state may have more than one senator on the committee ---->

if only 50 senators are available to form commitee , then 50c3 = 50*49*48/3*2*1 = 19600.

3) What’s the probability that no state will have both of its senators on a committee?---->
5/100*4/98*3/96*2/94*1/92= something im not interested in..
is the method ok??

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Intern
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Posts: 37

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31 Aug 2008, 20:58
why 50C3?

Should it be 50C5? Since we have 5 person committee?

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SVP
Joined: 07 Nov 2007
Posts: 1792

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Location: New York

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31 Aug 2008, 22:14
kamilaak wrote:
I am having problems with this question:

The US Senate consists of 100 senators, two from each state. A committee consisting of five senators is to be formed.

(a) How many different committees are possible?
(b) How many committees are possible if no state may have more than one senator on the committee?
(c) What’s the probability that no state will have both of its senators on a committee?

I think the first (a) should be: 100*99*98*97*96

But I'm not sure about (b) and (c). Help.

a)
100C5
b)

= 100*98*96*94*92 /5!
(First we can chose any senator(100 ways)* (one senator already chosen and we can't chose another senator from the same state so 98 members left)*....)

c)

p = (100*98*96*94*92 /5! ) / 100C5

What is OA
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Last edited by x2suresh on 04 Sep 2008, 07:19, edited 1 time in total.

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Current Student
Joined: 11 May 2008
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31 Aug 2008, 23:01
oh!!, yes i meant 50c5..

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Manager
Joined: 22 Jul 2008
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03 Sep 2008, 15:54
1) 100 C 5

2) 50 C 5 * (2 C 1)^5

3) 2)/1) i.e., 50 C 5 * (2 C 1)/100 C 5

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Re: Permutations???   [#permalink] 03 Sep 2008, 15:54
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