Question

in a race in which 9 contestants are entered in how many ways can first second and third place be awarded

Answer 1

Answer: 504 different ways.

Explanation:

This situation uses a permutation. We will use the given formula and simplify to solve. n is equal to the number of contestants and r is 3 since we are selecting and first-, second-, and third-place winner.

Given:

`\displaystyle P = (n!)/((n-r)!)`

Substitute values:

`\displaystyle P = (9!)/((9-3)!)`

Subtract:

`\displaystyle P = (9!)/(6!)`

Multiply:

`\displaystyle P = (9*8*7*6*5*4*3*2*1)/(6*5*4*3*2*1)`

Simplify using the knowledge that something divided by itself is 1:

P = 9 * 8 * 7

Multiply:

P = 504

We can also think of it as 9 different people could win 1st, 8 different people could win 2nd, and 7 different people could win 3rd. 9 * 8 * 7 = 504. However, the steps above show why this works with the formula as well.