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

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

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18 Oct 2006, 13:47
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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
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18 Oct 2006, 13:51
I am pretty sure it is C but I cannot really give a good explanation.
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18 Oct 2006, 14:49
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
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18 Oct 2006, 15:00
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

I agree...just another post had the answer as 60. Thanks
VP
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18 Oct 2006, 18:31
answer is D 60.

Categorize the race to 4 cases:
J is 1st, 2nd, 3rd, 4th. then sum up.
Manager
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18 Oct 2006, 19:30
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
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19 Oct 2006, 02:17
Yes should be D...

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

10*3!=60
19 Oct 2006, 02:17
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# John and bill are among five runners in a race where there

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