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# John and bill are among five runners in a race where there

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Intern
Joined: 23 Aug 2006
Posts: 26
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John and bill are among five runners in a race where there [#permalink]  18 Oct 2006, 13:47
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Question Stats:

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John and bill are among five runners in a race where there are no ties. How many ways is it possible for John to finish the race ahead of Bill?

A) 5
B) 10
C) 30
D) 60
E) 120
Manager
Joined: 04 Oct 2006
Posts: 189
Followers: 1

Kudos [?]: 1 [0], given: 0

I am pretty sure it is C but I cannot really give a good explanation.
Senior Manager
Joined: 30 Aug 2006
Posts: 374
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Kudos [?]: 19 [0], given: 0

10, not particularly elegant but...

1st - Jxxxx (4 spaces for Bill)
2nd - Jxxx (3)
3rd - Jxx (2)
4th - Jx (1)

4+3+2+1 = 10
Intern
Joined: 23 Aug 2006
Posts: 26
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londonluddite wrote:
10, not particularly elegant but...

1st - Jxxxx (4 spaces for Bill)
2nd - Jxxx (3)
3rd - Jxx (2)
4th - Jx (1)

4+3+2+1 = 10

VP
Joined: 25 Jun 2006
Posts: 1175
Followers: 2

Kudos [?]: 71 [0], given: 0

Categorize the race to 4 cases:
J is 1st, 2nd, 3rd, 4th. then sum up.
Manager
Joined: 25 Sep 2006
Posts: 153
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Kudos [?]: 4 [0], given: 0

I thought 10 at first.. but wait........

u guys have been ignoring the other 3 participants. By taking account for them, u should get 60
Director
Joined: 05 Feb 2006
Posts: 902
Followers: 1

Kudos [?]: 49 [0], given: 0

Yes should be D...

10 ways when John is ahead of Bill
3! ways for the other guys to mix up....

10*3!=60
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