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Probability Club

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Manager
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Probability Club [#permalink]

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New post 22 Jun 2009, 11:24
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The X fraternity must choose a delegation of three senior members and two junior members for an annual intrafaternity conference. If X fraternity has 12 Senior members and 11 Junior members, How many different delegations are possible?

I would aprecciate your answer explanation

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Re: Probability Club [#permalink]

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New post 22 Jun 2009, 12:05
This is a combinations problem.

\(C^n_k = \frac{n!}{k!(n-k)!}\)

where \(n\) = total number of items available to select and \(k\) = number of items to be selected.

In this problem there are two distinct sets: 1 set of senior members and 1 set of junior members.

The number of ways we can select 3 (\(k\)) senior members from a total of 12 (\(n\)) senior members:

\(\Rightarrow C^n_k = \frac{n!}{k!(n-k)!}\)

\(\Rightarrow C^{12}_3 = \frac{12!}{3!(12-3)!}\)

\(\Rightarrow C^{12}_3 = \frac{12!}{3!9!}\)

\(\Rightarrow C^{12}_3 = \frac{12 \times 11 \times 10}{3 \times 2} = 220\)

Similarly the number of ways we can select 2 (\(k\)) junior members from a total of 11 (\(n\)) junior members:

\(\Rightarrow C^n_k = \frac{n!}{k!(n-k)!}\)

\(\Rightarrow C^{11}_2 = \frac{11!}{2!(11-2)!}\)

\(\Rightarrow C^{11}_2 = \frac{11!}{2!9!}\)

\(\Rightarrow C^{11}_2 = \frac{11 \times 10}{2} = 55\)

Total number of different delegations of senior and junior members possible:

\(= 220 \times 55\)

\(= 12100\)

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Manager
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Re: Probability Club [#permalink]

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New post 22 Jun 2009, 12:06
12C3+11C2

220+55=275

Intrafraternity consists of 3 senior members from a pool of 12 senior members, so 12C3 and 2 junior members from a pool of 11 members so 11C2.

we add both the combinations to get 275 different types of delegations.

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New post 22 Jun 2009, 14:58
The answer is 220*55 = 12100.

what is OA?

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New post 23 Jun 2009, 07:45
nookway

You are right

thanks a lot

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Senior Manager
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Re: Probability Club [#permalink]

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New post 23 Jun 2009, 07:50
The answer is 220*55 = 12100.

Kudos [?]: 133 [0], given: 80

Re: Probability Club   [#permalink] 23 Jun 2009, 07:50
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