Question: In how many ways can 5 different prizes be distributed among 3 students?
Options:
243
125
60
30
Correct Answer: 243
Solution:
The number of ways to distribute 5 different prizes among 3 students is 3^5 = 243.
In how many ways can 5 different prizes be distributed among 3 students?
Practice Questions
Q1
In how many ways can 5 different prizes be distributed among 3 students?
243
125
60
30
Questions & Step-by-Step Solutions
In 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, we have 3 choices (one for each student).
Step 4: Since there are 5 prizes, and each prize can go to any of the 3 students, we multiply the choices for each prize.
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.
Combinatorics – The problem involves distributing distinct items (prizes) to distinct recipients (students), which is a fundamental concept in combinatorial mathematics.
Counting Principles – The solution applies the multiplication principle of counting, where each prize can be given to any of the students independently.
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