In a raffle 5 winners get to chose from 5 prizes starting with the fist name drawn. iIf 87 people entered the raffle how many ways can the winners be arranged?

$4 , 433 , 982 , 840 \text{ }$ ways

Explanation:

There are 87 ways to win the first prize
There are 86 ways to win the second prize
There are 85 ways to win the third prize
There are 84 ways to win the fourth prize
There are 83 ways to win the fifth prize

number of ways$= 87 \cdot 86 \cdot 85 \cdot 84 \cdot 83 = 4 , 433 , 982 , 840 \text{ }$

God bless....I hope the explanation is useful.