Question

there are 8 woman running in a race. how many different ways could, first, second, and third place finishers occur?

Answer 1

336

Explanation:

It is given that
`8` woman are running in a race.

The number of ways in which we can choose first position is
`8`.

The number of ways in which we can choose second position after choosing first position is
`7`.

This is because,there can be
`8` women to finish second,but since one woman is already chosen to finish first,there can be only
`7` now.

Using similar discussion,The number of ways in which we can choose third position after choosing first position is
`6`.

So,
`\text{total number of ways}=\text{number of ways position 1 is chosen}*\\\text{number of ways position 2 is chosen}* \text{number of ways position 3 is chosen}`

So,
`\text{total number of ways}=8* 7* 6=336`

So,there are
`336` ways to choose first,second an third positions when
`8` women are racing.