Respuesta :
Answer:
The number of ways to award the prizes if it satisfies the given conditions is 94,109,400.
Step-by-step explanation:
There are 100 tickets that are distributed among 100 different people.
Four different prizes are awarded, including a grand prize.
The selection of the four wining tickets can be done using permutations.
Permutation is an arrangement of all the data set in a specific order.
The formula to compute the permutation of k objects from n different objects is:
[tex]^{n}P_{k}=\frac{n!}{(n-k)!}[/tex]
In this case we need to compute the number of selection of the 4 winning tickets accordingly from 100 tickets.
Compute the number of ways to select 4 winning tickets as follows:
[tex]^{n}P_{k}=\frac{n!}{(n-k)!}[/tex]
[tex]^{100}P_{4}=\frac{100!}{(100-4)!}[/tex]
[tex]=\frac{100!}{96!}[/tex]
[tex]=\frac{100\times99\times98\times97\times96!}{96!}[/tex]
[tex]=94109400[/tex]
Thus, the number of ways to award the prizes if it satisfies the given conditions is 94,109,400.
