how many ways can we award a 1st, 2nd, and 3rd place prize among eight contestants? A) 336 B.) 56 C.) none of these D.) 40320

the answer is A. 336

Explanation:

There are 8 choices for awarding first prize. Then there are 7 choices for awarding second prize. And there are 6 choices for awarding third prize.

Therefore, there are: 8 * 7 * 6 = 336 ways.

The ways 1st - 3rd place are ordered matter, so we aren't finding the combination. We; re finding the permutation. This means we have 8 contestants taken 3 ways. The number of permutations of n objects taken r at a time is nPr = n! / (n - r) ! N is 8 and 3 is R. Substitute the values.

8P3 = 8! / (8 - 3) ! → 8! / 5! → 336

(You can also input this in a scientific calculator by pressing "8", then "nPr" then "3")