Question

In the Massachusetts Mass Cash game, a player chooses five distinct numbers from 1 to 35. In how many ways can a player select the five numbers?

Answer 1

A player can select the five numbers in 38,955,840 ways.

Explanation:

The order is important, for example

The sequence 1-35-32-33-34 is a different sequence than 35-1-32-33-34. Also, the elements cannot be repeated. So we use the permutations formula:

Permutations formula:

The number of possible permutations of x elements from a set of n elements is given by the following formula:

`P_((n,x)) = (n!)/((n-x)!)`

In this problem, we have that:

There are 35 numbers from 1 to 35, so
`n = 35`

We are choosing 5 elements, so
`x = 5`

In how many ways can a player select the five numbers?

`P_((n,x)) = (n!)/((n-x)!)`

`P_((35,5)) = (35!)/((30)!)) = 38,955,840`

A player can select the five numbers in 38,955,840 ways.