1. (Combinations) In Maryland\'s lottery, players pick six different integers be
ID: 2922853 • Letter: 1
Question
1. (Combinations) In Maryland's lottery, players pick six different integers between 1 and 49 inclusive (order does not matter). The lottery commission picks 6 of these randomly as the winning numbers. If you play the lottery, you will win the grand prize if you guess all six numbers correctly, the second prize if you guess exactly 5 of the winning numbers correctly, and the third prize if you guess exactly 4 of the winning numbers. Assuming you play just once, what is the probability you will win
(a) The grand prize?
(b) The second prize?
(c) The third prize?
Explanation / Answer
(a) There is only one way to get all the 6 numbers and so the probability
= 1 / 49C6
= 1 / 13983816
= 0.00000007
(b) The 5 numbers can be got in 6C5 = 6 ways.
Probability = 6 / 13983816
= 0.00000042
(c) The 4 numbers can be got in 6C4 = 15 ways.
Probability = 15 / 13983816
= 0.00000105.
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