In a lottery game, the jackpot is won by selecting five different whole numbers

Question

In a lottery game, the jackpot is won by selecting

five

different whole numbers from 1 through

40

and getting the same

five

numbers (in any order) that are later drawn. In the Pick

5

game, you win a straight bet by selecting

five

digits (with repetition allowed), each one from 0 to 9, and getting the same

five

digits in the exact order they are later drawn. The Pick

5

game returns

$50,000

for a winning $1 ticket. Complete parts (a) through (c) below.a. In a lottery game, the jackpot is won by selecting

five

different whole numbers from 1 through

40

and getting the same

five

numbers (in any order) that are later drawn. What is the probability of winning a jackpot in this game?P(winning a jackpot in this

game)equals=nothing

(Type an integer or a simplified fraction.)

Explanation / Answer

Since we have to choose 5 different numbers from 1 to 40, and since the order does not matter, so combination rule must be used. Possible 7 numbers out of 40 numbers is:

40C7 = 18,643,560

Out of 18,643,560 ways, there is only one way corresponding to Jackpot, so, the probability of jackpot is:

P(Jackpot) = 1/ 18,643,560

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