Question

In the cash now lottery game there are 6 finalists who submitted entry tickets on time. from these 6 tickets, three grand prize winners will be drawn. the first prize is one million dollars, the second prize is one hundred thousand dollars, and the third prize is ten thousand dollars. determine the total number of different ways in which the winners can be drawn. (assume that the tickets are not replaced after they are drawn.)

Answer 1

120 You have 6 tickets, so they can be arranged 6! ways (1*2*3*4*5*6 = 720). From an arrangement, you select the 1st 3 tickets. However, after you've picked the 1st 3 tickets, you have 3 tickets left that you really don't care about their order. So you divide the 720 possible arrangements by 3! which is 6. So the number of possible ways you can select the 3 winners is 6!/3! = 720/6 = 120

Answer 2

120 total number of different ways in which the winners can be drawn.

Explanation:

You have three prizes:

P1 - P2 - P3

There is no replacement for the tickets, so:

P1 can be any of the finalists. So there are 6 possible outcomes for P1.

P2 can be any of the finalists, bar P1. So there are 5 possible outcomes for P2.

P3 can be any of the remaining finalists, so 4 possible outcomes.

So

6 - 5 - 4

In all there are 6*5*4 = 120 total number of different ways in which the winners can be drawn.