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 68. (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

You have a total of 68 numbers to choose from.

Choosing 5 from 68 has 68C5 ways....i.e. =10424128 ....and as there is only one unique way you can get this the probability is:

1/10424128=0.00000010

Matching 4 of the 5 numbers means that 1 is not matched.

i.e. (5C4)(64C1).....so, combinations of choosing 4 from 5 multiplied by the combinations of not choosing the remaining 1 number from the 64 that are left.

=> probability is (5C4)(64C1)/(68C5) =5*64/10424128=0.00003070
P(Big winner OR Small winner) = P(Big) + P(Small) =0.00003080

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