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.)

Question

Mathematics

Fletcher Benson

10 February, 10:13

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.)

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John Gonzales · 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