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ps: football - mgmat challenge

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Manager
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New post 24 Sep 2007, 17:34
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Manhattan GMAT’s football team has 99 players. Each player has a uniform number from 1 to 99 and no two players share the same number. When football practice ends, all the players run off the field one-by-one in a completely random manner. What is the probability that the first four players off the field will leave in order of increasing uniform numbers (e.g., #2, then #6, then #67, then #72, etc)?

(A) 1/64
(B) 1/48
(C) 1/36
(D) 1/24
(E) 1/16
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New post 24 Sep 2007, 21:41
I think D...took me a while and i'm not sure if this is correct.

My reasoning is:

the size of the team is irrelevant. There are 4!=24 ways that the 4 jersey numbers of the first 4 players can be ordered. However since each number is distinct, there is only permutation in which the 4 numbers are in increasing order. Thus the probability is 1/24.
  [#permalink] 24 Sep 2007, 21:41
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