To determine the number of ways we can select four door prizes from eight different ones and distribute them among four people, we can follow these steps:
1. Calculate the number of ways to choose four prizes out of eight: This can be done using the combination formula. The number of ways to choose 4 prizes out of 8 is given by C(8,4) = 8! / (4!(8-4)!) = 70 ways.
2. Distribute the selected prizes among the four people: Since each person can receive one prize, the number of ways to distribute the four selected prizes among four people is 1 way, as each person will receive one prize.
Therefore, the total number of ways to select four door prizes from eight different ones and distribute them among four people is 70.
