A state lottery is conducted in which six winning numbers are randomly selected

Question

A state lottery is conducted in which six winning numbers are randomly selected from a total of 54 numbers. If you selected six numbers, what is the probability that you will select

-All six winning numbers

-Five winning numbers

-Four winning numbers

-None of the winning numbers

-What is the average number of winning numbers that you would expect to select.

(obviously i can put it into excel and recieve these answers but i also need to know how to work them out in case this ends up on an exam with no laptop)

thank you ahead of time

Explanation / Answer

All six winning numbers is1/54c6=3.07e-8

Five winning numbers is 1/54c5=2.61e-7

Four winning numbers is 1/54c4=3.16e-6

None is 1-3.07e-8.

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