Question

There are 4 cyclists in a race. There will be a first place, a second place, and a third place prize awarded. In how many different ways can the 3 prizes be awarded?

Answer 1

The number of ways can the 3 prizes be awarded = 4 ways

Explanation:

It is given that,

There are 4 cyclists in a race. There will be a first place, a second place, and a third place prize awarded.

To find the possible number of ways

There are 4 cyclists

The number of prizes = 3

The number of ways can the 3 prizes be awarded = 4C₃

To find 4C₃

4C₃ = (4 * 3 * 2)/(1 * 2 * 3) = 4 ways

Therefore the number of ways can the 3 prizes be awarded = 4 ways

Answer 2

24 ways

Explanation:

We are given that there 4 cyclists in a race and there will be first, second and third place awards for them.

We are to find out the number of ways these prizes can be awarded. For this, we will use the following formula:

`nPr= (n!)/((n-r)!)`

Substituting the values in the above formula to get:

`_4 P_3 = \frac { 4! } { ( 4 - 3 ) !} = \frac { 4 * 3 * 2 * 1} {1} =24`

Therefore, the three prizes can be awarded in 24 ways.