Need approach for this problem

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Tryingmybest: Master | Next Rank: 500 Posts; Posts: 168; Joined: Thu Nov 13, 2008 4:34 am; Location: Pittsburgh; Thanked: 9 times

Need approach for this problem

by Tryingmybest » Tue Mar 24, 2009 11:05 am

I came across this question in Princeton . Unfortunately I reset the test. Please help me with the approach to this problem.

What is the probability of choosing four numbers 1, 2, 3, and 4 by four different persons A,B , C and D such that every Person chooses a distinct number?

I dont have a OA for this problem. But would like to know the approach.
Thanks!

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Source: Beat The GMAT — Problem Solving | Tue Mar 24, 2009 11:05 am

devesh99: Junior | Next Rank: 30 Posts; Posts: 14; Joined: Wed Feb 18, 2009 4:56 pm; Thanked: 1 times

by devesh99 » Tue Mar 24, 2009 12:56 pm

Just trying

For selection of distinct numbers:
A can choose any of the 4 numbers (1,2,3,4) = 4
B can choose from any of the 3 remaining numbers = 3
C can choose from any of the 2 remaining numbers = 2
D can choose the last remaining number = 1
Therefore, 4*3*2*1 = 24

Now, for selection of numbers
A can select any of the 4 numbers = 4
B can select any of the 4 numbers = 4
C can select any of the 4 numbers = 4
D can select any of the 4 numbers = 4
Total chances = 4*4*4*4

Therefore Prability = 24/26 = 3/32