SOLUTION: in how many different ways the first 3 places can be filled in a race in which there are 11 horses

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Question 253686: in how many different ways the first 3 places can be filled in a race in which there are 11 horses
Found 2 solutions by vleith, edjones:
Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
think of it this way. How many horse could finish first?
11
How many could be second once the horse given one horse was already first?
11-1 = 10
How may could be third given that two horses finished ahead of them
11-2 = 9
So how many different can the first three places be filled?
11*10*9

Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
We are interested in the ways the horses can be arranged (1st, 2nd or 3rd) so this is a permutation question.
nPr=n!/(n-r)!
.
11P3=11!/(11-3)!=11!/8!=(11*10*9*8!)/8!=11*10*9=990 different ways.
.
Ed