Probability Problem

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sands_of_time: Junior | Next Rank: 30 Posts; Posts: 21; Joined: Tue Apr 07, 2009 4:47 am

by sands_of_time » Mon Apr 27, 2009 12:34 am

As part of a game, four people each must secretly choose an integer between 1 and 4, inclusive. What is the approximate likelihood that all four people will choose different numbers ?

a) 9%
b) 12%
c) 16%
d) 20%
e) 25%

Please help me with this problem.

OA A

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Source: Beat The GMAT — Problem Solving | Mon Apr 27, 2009 12:34 am

ketkoag: Legendary Member; Posts: 876; Joined: Thu Apr 10, 2008 8:14 am; Thanked: 13 times

by ketkoag » Mon Apr 27, 2009 1:04 am

possibility of all the 4 choose different nos(event) : 4 * 3 * 2 * 1
possibility of all the 4 choose any no. (sample space) : 4 * 4 * 4 * 4

answer choices are in % so multiply event/SS by 100 to get the approximate answer.

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bluementor: Master | Next Rank: 500 Posts; Posts: 418; Joined: Wed Jun 11, 2008 5:29 am; Thanked: 65 times

by bluementor » Mon Apr 27, 2009 1:06 am

No. of ways 4 people can choose 4 integers = 4x4x4x4
No. of ways 4 people can choose different integers = 4x3x2x1

Prob of 4 people choosing different integers =

(4x3x2x1)/(4x4x4x4) = 3/32 ≈ 9%

Choose A.

-BM-

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