Question

ak uhd ttreprinted by permission of Npaper Enterprise Association, Inc. 10. Most lotteries include several prizes besides the jackpot. For example, the current Florida lottery gives second prizes to tickets that match 5 of the 6 winning numbers, third prizes to those that match 4 of the 6, and fourth prizes to those that match 3 of the 6 a. How many different ways are there to receive a second prife (Hint: The ticket must match 5 of the 6 winning numbers and 1 a. C. of the 47 non-winning numbers.) b. How many different ways are there to receive a third prize? c. How many different ways are there to receive a fourth prize? 14. En of

Answer 1

Here it is given current Florida lottery gives second prize to tickets that match 5 of the 6 winning numbers and 1 of the 47 non - winning numbers (Given) Hence, there a 6 winning numbers and 47 non - winning numbers. Total of 53 numbers. Total number of ways tot select a six number ticket rightarrow 53_c_6 In these 53_c_6 tickets there are some tickets which will win second prize. Condition CF second prize is it should match 5 of 6 winning numbers and 1 out of 47 non- winning numbers. Let us first consider there are 6 winning numbers. Now 6_c_5 are the number of ways, that 5 numbers out of 6 will match. And 47_c_1 will be the number of ways, that 1 number out of 47 will be selected or not matched. Hence combining both conditions, we get 6_c_5 times 47_c_1 = ANS