To win at LOTTO in one​ state, one must correctly select 5 numbers from a collection of 54 numbers​ (1 through 54​). The order in which the selection is made does not matter. How many different selections are​ possible?

Answer 1

To calculate the number of different selections possible, we can use the combination formula:

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

where n is the total number of numbers to choose from (in this case, 54), and r is the number of numbers to be chosen (in this case, 5).

Plugging in the values, we get:

54C5 = 54! / 5!(54-5)!
= 54! / 5!49!
= (54 * 53 * 52 * 51 * 50) / (5 * 4 * 3 * 2 * 1)
= 25,827,165

Therefore, there are 25,827,165 different selections possible when choosing 5 numbers from a collection of 54 numbers without regard to the order in which the selection is made.