Question

Set up the problem, but use a calculator to find the number of outcomes for the permutation. Eight horses run a race. In how many ways can the first three finishers turn out?

Answer 1

Answer:  336

Explanation:

Label the slots A,B,C for first through third place.

There are 8 choices for slot A, 7 for slot B, and 6 for slot C. We start with 8 and count our way down until we get to the final slot. Then we multiply out those values

8*7*6 = 336

There are 336 ways to select three people from a pool of eight overall.

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If you want to use the permutation formula, then your steps might look like this

$_n P _r = \frac{n!}{(n-r)!}\\\\_8 P _3 = \frac{8!}{(8-3)!}\\\\_8 P _3 = \frac{8!}{5!}\\\\_8 P _3 = \frac{8*7*6*5!}{5!}\\\\_8 P _3 = 8*7*6\\\\_8 P _3 = 336$

Note how the 5! terms cancel out on the second to last step, leaving behind the expression 8*7*6 which was found earlier.