Question

How many ways can first, second, and third place be assigned?At a gymnastics meet, twenty gymnasts compete for first, second, and third place.

Answer 1

The correct answer is

1. 6,840

2. 342

3. 18

At a gymnastics meet, twenty gymnasts compete for first, second, and third place.

Answer 2

The total number of ways can first, second and third place can be assigned are:

6840

Explanation:

The total number of people that compete are: 20

Out of these 20 people we have to chose 3 people and also arrange them according to their ranks.

We know that when we have to choose and arrange r items out of total n items then we need to use the method of permutation.

Hence, the formula is given by:

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

Here we have:

n=20 and r=3

Hence, the number of ways first, second and third place can be assigned are:

`{20}_P_3=(20!)/((20-3)!)\\\\\\{20}_P_3=(20!)/(17!)\\\\\\{20}_P_3=(20* 19* 18* 17!)/(17!)\\\\\\{20}_P_3=20* 19* 18\\\\\\{20}_P_3=6840`

Hence, the answer is:

6840