A state lottery game requires a person to select nine different numbers from thirty-six numbers.The order of the selection is not important.In how many ways can this be done?

Question

Quizplus · Accepted Answer

This problem involves using the combination formula. We have 36 numbers to choose from, and we want to select 9 of them. The order in which we select them does not matter, so we use the combination formula:
$${{n}\choose{k}}=\frac{n!}{k!(n-k)!}$$
Plugging in the numbers we get:
$${{36}\choose{9}}=\frac{36!}{9!(36-9)!}=\frac{36!}{9!27!}=126,843,969$$
Therefore, there are 126,843,969 ways to select nine different numbers from thirty-six numbers. The best choice is C.

A State Lottery Game Requires a Person to Select Nine