In the Cash Now lottery game there are 19 finalists who submitted entry tickets on time. From these 19 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.)

There are 5,814 ways to select the three winners.

Step-by-step explanation:

Total number of tickets submitted is, n = 19.

Three winners are to selected from these 19.

There are no conditions applied for the selection procedure.

That is, the 3 winners are selected randomly.

It is also provided that the tickets are not replaced after they are drawn.

The number of ways to select the first winner is, 19 ways.

Remaining tickets: 19 - 1 = 18.

The number of ways to select the second winner is, 18 ways.

Remaining tickets: 18 - 1 = 17.

The number of ways to select the third winner is, 17 ways.

The total number of ways to select 3 winners is:

Thus, there are 5,814 ways to select the three winners.

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