Question 231056: Hello,
I always have trouble with word problems and I just want to make sure that I am doing this one correctly:
Eight horses are entered into a race. In how many ways can they cross the finish line, if ties are not allowed?
is it: 8*8*8*8*8*8*8*8 (8^8)
thank you for your help,
Peter
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 8 horses can cross the finish line in 8! ways.
Consider 3 horses.
3! = 3*2*1 = 6 ways they can cross the finish line.
Those ways would be:
123
132
213
231
312
321
Now consider 4 horses in a race.
The number of ways they can cross the finish line is 4!
4! = 4*3*2*1 = 24
Those ways are:
1234
1243
1324
1342
1423
1432
----
2134
2143
2314
2341
2413
2431
----
There should be 2 more sets of 6 which would make a total of 24.
I'll do them just to show you.
----
3124
3142
3214
3241
3412
3421
----
4123
4132
4213
4231
4312
4321
----
I think that does it.
For your problem, the numbers are too high to show each one separately, but the formula looks like it will do the trick so your answer is:
8! which equals 8*7*6*5*4*3*2*1
That equals 40,320 ways.
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