Question

Twenty dash three people purchase raffle tickets. Three winning tickets are selected at random. If first prize is ​$1000​, second prize is ​$500​, and third prize is ​$100​, in how many different ways can the prizes be​ awarded?

Answer 1

Answer: 10626

Step-by-step explanation:

Given : The total number of people purchase raffle tickets=23

The total number of prizes = 3

Since , order matters here , so we use Permutations.

The permutation of n things taken r at a time is given by :-

$^nP_r=\dfrac{n!}{(n-r)!}$

Then, the number of ways the prizes can be distributed :-

$^{23}P_{3}=\dfrac{23!}{(23-3)!}\\\\=\dfrac{23\times22\times21\times20!}{20!}=10626$

Hence, the prizes can be distributed in 10626 ways.