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17 May 2007, 17:43
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If you have five runners, John, James, Rick, Jessica, and Ryan, running a 100-yard dash, in how many ways can the runners finish in which James finishes before Jessica (and no ties are possible).
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17 May 2007, 19:27
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ethan_casta
= 60
James = a
Jessica = b
John = 1
Rick = 2
Ryan = 3
ab123 = 6
1ab23 = 6
12ab3 = 6
123ab = 6
a1b23 = 6
a12b3 = 6
a123b = 6
1a2b3 = 6
1a23b = 6
12a3b = 6
total = 60
Updated on: 18 May 2007, 11:09
Originally posted by KillerSquirrel on 18 May 2007, 02:27.
Last edited by KillerSquirrel on 18 May 2007, 11:09, edited 2 times in total.
Last edited by KillerSquirrel on 18 May 2007, 11:09, edited 2 times in total.
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the question isn't clear
if we have 5 places , can James be first and Jessica fifth ? or Jassica has to be second.
when James first and jassica has to be second:
4! = 4*3*2= 24
John, James, Rick, Jessica, and Ryan
since James has to be before Jessica
the we look at James-Jessica as one
so total ways of all of them is 5!, and if James-Jessica is one then 4!
when James first and jassica can be second,third and so on...
4! + 6*3+6*2+6*1 = 60
4! - see above
6*3 = 18
6*2 = 12
6*1 = 6
explanation:
when James first jassica can be third,fourth,fifth - no. of times James can be first = 6 , no. of ways jassica can be third,fourth, fifth = 3
when James second jassica can be third,fourth,fifth - no. of times James can be second = 6 , no. of ways jassica can be fourth, fifth = 2
when James second jassica can be third,fourth,fifth - no of times James can be third = 6 , no. of ways jassica can be fifth = 1
then the answer is 60 (was edited !)
if we have 5 places , can James be first and Jessica fifth ? or Jassica has to be second.
when James first and jassica has to be second:
4! = 4*3*2= 24
John, James, Rick, Jessica, and Ryan
since James has to be before Jessica
the we look at James-Jessica as one
so total ways of all of them is 5!, and if James-Jessica is one then 4!
when James first and jassica can be second,third and so on...
4! + 6*3+6*2+6*1 = 60
4! - see above
6*3 = 18
6*2 = 12
6*1 = 6
explanation:
when James first jassica can be third,fourth,fifth - no. of times James can be first = 6 , no. of ways jassica can be third,fourth, fifth = 3
when James second jassica can be third,fourth,fifth - no. of times James can be second = 6 , no. of ways jassica can be fourth, fifth = 2
when James second jassica can be third,fourth,fifth - no of times James can be third = 6 , no. of ways jassica can be fifth = 1
then the answer is 60 (was edited !)
