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

Answer:

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

Answer:

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

                          6840

Step-by-step 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:

$n_P_r=\dfrac{n!}{(n-r)!}$

Here we have:

n=20 and r=3

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

${20}_P_3=\dfrac{20!}{(20-3)!}\\\\\\{20}_P_3=\dfrac{20!}{17!}\\\\\\{20}_P_3=\dfrac{20\times 19\times 18\times 17!}{17!}\\\\\\{20}_P_3=20\times 19\times 18\\\\\\{20}_P_3=6840$

         Hence, the answer is:

                 6840