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# Probability Club

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Manager
Joined: 29 May 2008
Posts: 110

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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?

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Current Student
Joined: 03 Aug 2006
Posts: 112
Location: Next to Google
Schools: Haas School of Business
Re: Probability Club [#permalink]

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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:

$$= 220 \times 55$$

$$= 12100$$
Manager
Joined: 15 Apr 2008
Posts: 159
Re: Probability Club [#permalink]

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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.
Intern
Joined: 04 Mar 2008
Posts: 42
Re: Probability Club [#permalink]

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

what is OA?
Manager
Joined: 29 May 2008
Posts: 110
Re: Probability Club [#permalink]

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23 Jun 2009, 07:45
nookway

You are right

thanks a lot
Senior Manager
Joined: 23 Jun 2009
Posts: 355
Location: Turkey
Schools: UPenn, UMich, HKS, UCB, Chicago
Re: Probability Club [#permalink]

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

--== Message from GMAT Club Team ==--

This is not a quality discussion. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

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

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