Question

In how many ways can a judge award first, second, and third places in a contest with 10 entries?

1,000

720

30

Answer 1

the answer is : 30 different ways

Answer 2

The number of ways a judge can award first, second, and third places in a contest with 10 entries is:

720

Explanation:

We know that the choosing and arranging of r entries out of a total of n entries is given by the method of permutation and the formula is given by:

`n_P_r=(n!)/((n-r)!)`

Here we have to chose and arrange 3 people according to their ranks out of a total of 10 entries.

i.e. r=3 and n=10

Hence, the formula is given by:

`{10}_P_3=(10!)/((10-3)!)\\\\\\{10}_P_3=(10!)/(7!)\\\\\\{10}_P_3=(10* 9* 8* 7!)/(7!)\\\\\\{10}_P_3=10* 9* 8\\\\\\{10}_P_3=720`

Hence, the answer is:

720 ways