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

Answer:

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

Step-by-step 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:

$P_{(n,x)} = \frac{n!}{(n-x)!}$

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?

$P_{(n,x)} = \frac{n!}{(n-x)!}$

$P_{(35,5)} = \frac{35!}{(30)!)} = 38,955,840$

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