Question

One hundred tickets, numbered 1, 2, 3, . . . , 100, are sold to 100 different people for a drawing. Four different prizes are awarded, including a grand prize (a trip to Tahiti). How many ways are there to award the prizes if it satisfies the given conditions.

Answer 1

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:

$^{n}P_{k}=\frac{n!}{(n-k)!}$

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:

 $^{n}P_{k}=\frac{n!}{(n-k)!}$

$^{100}P_{4}=\frac{100!}{(100-4)!}$

         $=\frac{100!}{96!}$

         $=\frac{100\times99\times98\times97\times96!}{96!}$

         $=94109400$

Thus, the number of ways  to award the prizes if it satisfies the given conditions is 94,109,400.