How many ways can 5 different prizes be distributed among 3 students?

How many ways can 5 different prizes be distributed among 3 students?

Correct Answer: 243

Step 1: Understand that we have 5 different prizes to give away.
Step 2: Recognize that there are 3 students who can receive these prizes.
Step 3: For each prize, think about how many choices we have. Since there are 3 students, each prize can go to any of the 3 students.
Step 4: Since there are 5 prizes and each prize has 3 choices, we multiply the choices for each prize together.
Step 5: This means we calculate 3 choices for the first prize, 3 choices for the second prize, and so on, up to the fifth prize.
Step 6: The total number of ways to distribute the prizes is 3 multiplied by itself 5 times, which is written as 3^5.
Step 7: Calculate 3^5, which equals 243. This is the total number of ways to distribute the 5 different prizes among the 3 students.

Combinatorial Distribution – The problem involves distributing distinct items (prizes) to distinct recipients (students), where each item can go to any recipient independently.