How many ways can 4 different prizes be awarded to 3 students?

How many ways can 4 different prizes be awarded to 3 students?

Correct Answer: 81

Step 1: Understand that we have 4 different prizes to give away.
Step 2: Recognize that there are 3 students who can receive these prizes.
Step 3: For each prize, we can choose any of the 3 students to receive it.
Step 4: Since there are 4 prizes, and each prize can go to any of the 3 students, we multiply the choices for each prize.
Step 5: This means we have 3 choices for the first prize, 3 choices for the second prize, 3 choices for the third prize, and 3 choices for the fourth prize.
Step 6: We can express this as 3 choices for each of the 4 prizes, which is calculated as 3^4.
Step 7: Calculate 3^4, which equals 81.
Step 8: Conclude that there are 81 different ways to award the 4 different prizes to the 3 students.

Combinatorics – The study of counting, arrangements, and combinations of objects.
Permutations and Distributions – Understanding how to distribute distinct items (prizes) among distinct groups (students).