Ten students are participating in a race. In how many ways can the first

To find: number of ways of winning the first three prizes

The first price can go to any of the 10 students.

The second price can go to any of the remaining 9 students.

The third price can go to any of the remaining 8 students.

Formula:

Number of permutations of $n$ distinct objects among $r$ different places, where repetition is not allowed, is

$P(n, r)=n ! /(n-r) !$

Therefore, a permutation of 10 different objects in 3 places is

$P(10,3)=\frac{10 !}{(10-3) !}$

$=\frac{10 !}{7 !}=\frac{3628800}{5040}=720$

Therefore, there are 10 × 9 × 8 = 720 ways to win first three prizes.