Question

A certain lottery has 37 numbers. In how many different ways can 5 of the numbers be selected? (Assume that order of selection is not important.) There are different ways the numbers can be selected (Simplify your answer.)

Answer 1

The number of different ways to select 5 numbers from a lottery of 37 is 153,393

Step-by-step explanation:

To find the number of different ways that 5 numbers can be selected from a lottery of 37 numbers, we can use the concept of combinations. In this case, order does not matter so we can use the formula for combinations. The formula for combinations is given by:

C(n, r) = n! / (r! * (n-r)!)

where n is the total number of items and r is the number of items to be selected. In this case, n = 37 and r = 5. So the number of different ways to select 5 numbers from 37 is:

C(37, 5) = 37! / (5! * (37-5)!) = 37! / (5! * 32!) = (37 * 36 * 35 * 34 * 33) / (5 * 4 * 3 * 2 * 1) = 153,393

Answer 2

The number of different ways to select 5 numbers out of 37 is 153,393.

Step-by-step explanation:

The number of different ways to select 5 numbers out of 37, when order is not important, can be calculated using combination formula. The formula for combination is given by:

nCr = n! / ((n-r)! * r!)

where n is the total number of options and r is the number of selections.

Using this formula, the number of ways to select 5 numbers out of 37 is:

37C5 = 37! / ((37-5)! * 5!)

Simplifying further, we get:

37C5 = (37 * 36 * 35 * 34 * 33) / (5 * 4 * 3 * 2 * 1) = 153,393