How many different ways can 3 winning tickets be selected from 50 tickets, without replacement, if
Each ticket wins a different prize? (Note: the tickets can be selected in any order.)
A)117,500
B)118,100
C)117,600
D)117,700

Question

Quizplus · Accepted Answer

The first winning ticket can be any of the 50 tickets. The second winning ticket can be any of the remaining 49 tickets. The third winning ticket can be any of the remaining 48 tickets. Thus, the total number of ways to select 3 winning tickets with different prizes is 50 x 49 x 48, which is equal to 117,600. Therefore, the best choice is C. There are 50 ways to choose the first ticket, 49 ways to choose the second ticket, and 48 ways to choose the third ticket (since one ticket has already been chosen each time). However, since the order in which the tickets are chosen doesn't matter, we need to divide by the number of ways to arrange the three tickets, which is 3! = 6. Therefore, the total number of ways to choose 3 winning tickets, without replacement and with each ticket winning a different prize, is (50*49*48)/6 = 117,600.

How Many Different Ways Can 3 Winning Tickets Be Selected