8. In a lottery, 6 balls are drawn randomly from a set of 49 balls numbered...
8. In a lottery, 6 balls are drawn randomly from a set of 49 balls numbered 1, 2, . . . , 49. You choose 6 numbers on your ticket, and you win if you have the same 6 numbers as the numbers of the balls that are drawn. It does not matter if your numbers are in the same order as the order the balls are drawn (order does NOT matter). We consider two different lottery rules in the following two parts.
(a) How many different possibilities are there for the lottery drawing if the balls are not replaced after they are drawn (so all 6 numbers must be different)?
(b) How many different possibilities are there for the lottery drawing if the balls are replaced after they are drawn (so you can repeat numbers)?
Homework Answers
Total numbers = 49
Hence,
a) Number of possibilities if balls are not replaced = 49*48*47*46*45*44 = 10068347520
b) Number of possibilities if balls are replaced = 49*49*49*49*49*49 = 13841287201
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