Question

The Sad State Lottery requires you to select a sequence of four different numbers from 0 through 39. (Order is important.) You are a Winner if your sequence agrees with that in the drawing, and you are a Booby Prize Winner if your selection of numbers is correct, but in the wrong order. (Enter your answers as exact answers.) What is the probability of being a Winner?

What is the probability of being a Booby Prize Winner?

What is the probability that you are either a Winner or a Booby Prize Winner?

Answer 1

Permutation formula: nPr = n!/(n-r)!

Combination formula: nCr = n!/(r! x (n-r)!)

P(being a Booby prize winner) = 1/(Number of permutations of 4 numbers from 40 - Number of combinations of 4 numbers from 40)

= 1/(40P4 - 40C4)

= 1/(2,193,360 - 91,390)

= 1/2,101,970

P(either a Winner or a Booby Prize Winner) = 1/Number of combinations of 4 numbers from 40

= 1/40C4

= 1/91,390