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

1.	Ten students are participating in a race. In how many ways can the first three prizes be won?
Answer» 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.

Ten students are participating in a race. In how many ways can the first three prizes be won?

Answer»

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.