How many ways can 4 different prizes be distributed among 3 students?

How many ways can 4 different prizes be distributed among 3 students?

Correct Answer: 81

Step 1: Identify the number of prizes. In this case, there are 4 different prizes.
Step 2: Identify the number of students. Here, there are 3 students.
Step 3: Understand that each prize can be given to any of the 3 students. This means for each prize, there are 3 choices.
Step 4: Calculate the total number of ways to distribute the prizes. Since there are 4 prizes and each can go to 3 students, you multiply the choices: 3 choices for the first prize, 3 for the second, 3 for the third, and 3 for the fourth.
Step 5: Use the formula for this situation, which is 3 (choices) raised to the power of 4 (prizes): 3^4.
Step 6: Calculate 3^4, which equals 81. This means there are 81 different ways to distribute the 4 prizes among the 3 students.

Combinatorial Distribution – This concept involves distributing distinct items (prizes) among distinct groups (students) where each item can go to any group.