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 <em>k</em> objects from <em>n</em> different objects is:
![^{n}P_{k}=\frac{n!}{(n-k)!}](https://tex.z-dn.net/?f=%5E%7Bn%7DP_%7Bk%7D%3D%5Cfrac%7Bn%21%7D%7B%28n-k%29%21%7D)
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)!}](https://tex.z-dn.net/?f=%5E%7Bn%7DP_%7Bk%7D%3D%5Cfrac%7Bn%21%7D%7B%28n-k%29%21%7D)
![^{100}P_{4}=\frac{100!}{(100-4)!}](https://tex.z-dn.net/?f=%5E%7B100%7DP_%7B4%7D%3D%5Cfrac%7B100%21%7D%7B%28100-4%29%21%7D)
![=\frac{100!}{96!}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B100%21%7D%7B96%21%7D)
![=\frac{100\times99\times98\times97\times96!}{96!}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B100%5Ctimes99%5Ctimes98%5Ctimes97%5Ctimes96%21%7D%7B96%21%7D)
![=94109400](https://tex.z-dn.net/?f=%3D94109400)
Thus, the number of ways to award the prizes if it satisfies the given conditions is 94,109,400.