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

Question

In a lottery? game, the jackpot is won by selecting six different whole numbers from 1 through 35 and getting the same six numbers? (in any? order) that are later drawn. In the Pick 3 ?game, you win a straight bet by selecting three digits? (with repetition? allowed), each one from 0 to? 9, and getting the same three digits in the exact order they are later drawn. The Pick 3 game returns ?$500 for a winning? $1 ticket. Complete parts? (a) through? (c) below. a. In a lottery? game, the jackpot is won by selecting six different whole numbers from 1 through 35 and getting the same six 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

Solution:

a. The number of ways of selecting 6 different whole numbers from 1 through 35 (in any order) is given as:

C (35, 6) = 39!/(6!*33!)

C (35, 6) = 1623160

The probability of winning a jackpot in this game is given as

1/1623160 = 0.000000616

b. The number of ways of selecting the first digit = 10

The number of ways of selecting the second digit with repetition allowed = 10

The number of ways of selecting the third digit with repetition allowed = 10

Total number of ways of selecting three digits (i.e. 0-9) with repetition allowed is given as:

Total number of ways=10×10×10=1000

Therefore, the probability of winning the game is 1/1000.

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