The Sorry State Lottery requires you to select five different numbers from 0 thr

Question

The Sorry State Lottery requires you to select five different numbers from 0 through 55. (Order is not important.) You are a Big Winner if the five numbers you select agree with those in the drawing, and you are a Small-Fry Winner if four of your five numbers agree with those in the drawing. (Enter your answers as exact answers.)

What is the probability of being a Big Winner?
__________________

What is the probability of being a Small-Fry Winner?
_____________

What is the probability that you are either a Big Winner or a Small-Fry Winner?

Explanation / Answer

Total number of possible combinations = 56C5 = 3819816

In this, all 5 numbers can get matched by only one way. Hence,

P(Big Winner) = 1/3819816

Similarly, 4 numbers can get matched in 5C4 i.e. 5 ways.

Hence,

P(Small - Fry Winner) = 5/3819816

So,

P(Either a Big - Winner or a Small - Fry Winner) = 1/3819816 + 5/3819816 = 6/3819816 = 1/636636

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