Question

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

Answer 1

The answer is : 30 different ways

Answer 2

Answer:

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

                                 720

Step-by-step 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:

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

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:

${10}_P_3=\dfrac{10!}{(10-3)!}\\\\\\{10}_P_3=\dfrac{10!}{7!}\\\\\\{10}_P_3=\dfrac{10\times 9\times 8\times 7!}{7!}\\\\\\{10}_P_3=10\times 9\times 8\\\\\\{10}_P_3=720$

                  Hence, the answer is:

                             720 ways