Question

In a cohort of 35 graduating students, there are three different prizes to be awarded. If no student can receive more than one prize, in how many different ways could the prizes be awarded?

Answer 1

We have been given in a cohort of 35 graduating students, there are three different prizes to be awarded. We are asked that in how many different ways could the prizes be awarded, if no student can receive more than one prize.

To solve this problem we will use permutations.

$_{r}^{n}\textrm{P}={_{3}^{35}\textrm{P}}$

We know that formula for permutations is given as

$_{r}^{n}\textrm{P}=\frac{n!}{(n-r)!}$

On substituting the given values in the formula we get,

${_{3}^{35}\textrm{P}}=\frac{35!}{(35-3)!}=\frac{35!}{32!}$

$=\frac{35\cdot 34\cdot 33\cdot 32!}{32!}\\ \\ =35\cdot 34\cdot 33=39270$

Therefore, there are 39270 ways in which prizes can be awarded.