The number of ways a judge can award first, second, and third places in a contest with 10 entries is:
720
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:
[tex]n_P_r=\dfrac{n!}{(n-r)!}[/tex]
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:
[tex]{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[/tex]
Hence, the answer is:
720 ways
