Question

A university has three table tennis scholarships each worth $1000. How many ways are there to award these after they've narrowed

the candidates to 6 ping pong players?
Blank 1:

Answer 1

1. In the presence of restrictions; A player cannot win more than one scholarship;

The number of ways is 120 ways

2. In the absence of restrictions; A player can win more than 1:

The number of ways is 216 ways

Explanation:

Here, to award the scholarships, the restrictions we might have is that a student cannot win more than 1 scholarship

Given this restriction;

The first scholarship has 6 possible contenders

The second has 5

The third has 4

So, the number of possible ways is;

6 * 5 * 4 = 120 ways

In the absence of no restrictions where a student can win any number of scholarships;

We have the 3 scholarships being awarded in 6 possible ways

So the total number of ways will be;

6 * 6 * 6 = 216 ways