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: 2193360Step-by-step explanation:Given : Total people = 40Number of winning tickets = 3When 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  :-[tex]^nP_m=\dfrac{n!}{(n-m)!}[/tex]For r= 3  and n= 40 , we have[tex]^{40}P_{4}=\dfrac{40!}{(40-4)!}\\\\=\dfrac{40\times39\times38\times37\times36!}{36!}=40\times39\times38\times37=2193360[/tex]Hence, the number of different ways can the prizes be​ awarded = 2193360