Question

FortyForty people purchase raffle tickets. Three winning tickets are selected at random. If first prize is ​$50005000​, second prize is ​$45004500​, and third prize is ​$500500​, in how many different ways can the prizes be​ awarded?

Answer 1

To determine the number of different ways the prizes can be awarded, we need to use the concept of combinations.

Step-by-step explanation:

To determine the number of different ways the prizes can be awarded, we need to use the concept of combinations. Since there are 40 people purchasing raffle tickets, and 3 winning tickets are selected at random, we can find the number of ways the prizes can be awarded using the formula for combinations:

C(n, r) = n! / ((n-r)! * r!)

Where n is the total number of items and r is the number of items chosen at a time. In this case, n = 40 and r = 3:

C(40, 3) = 40! / ((40-3)! * 3!)

= 40! / (37! * 3!)

= (40 * 39 * 38) / (3 * 2 * 1)

= 9880

Therefore, there are 9,880 different ways the prizes can be awarded.

Answer 2

Answer: 2193360

Step-by-step explanation:

Given : Total people = 40

Number of winning tickets = 3

When we choose m things from n things in an order then we use permutations to find the number of different ways to choose them.

Number of permutations of n things taking m at a time :-

`^nP_m=(n!)/((n-m)!)`

For r= 3 and n= 40 , we have

`^(40)P_(4)=(40!)/((40-4)!)\\\\=(40*39*38*37*36!)/(36!)=40*39*38*37=2193360`

Hence, the number of different ways can the prizes be​ awarded = 2193360