Question

8. In a lottery, ll lra knly from a alls mubl 1,2,...,19. 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)?

Answer 1

Sol a)

There are 49 balls of different number.

Drawing six balls of matching numbers on the ticket without replacement

Required number of ways =$\binom{49}{6}=13983816$

Ans b) when the balls are drawing with replacement

6 balls out of 49 can be drawn with replacement =$49^{6}=13841287201$

If The number can be in any order then 6!=720

Required number of ways =$13841287201*720$