Question: In how many ways can 5 different trophies be awarded to 3 students?
Options:
60
100
30
20
Correct Answer: 60
Solution:
The number of ways to award 5 trophies to 3 students is 3^5 = 243.
In how many ways can 5 different trophies be awarded to 3 students?
Practice Questions
Q1
In how many ways can 5 different trophies be awarded to 3 students?
60
100
30
20
Questions & Step-by-Step Solutions
In how many ways can 5 different trophies be awarded to 3 students?
Correct Answer: 243
Step 1: Understand that we have 5 different trophies to give away.
Step 2: Recognize that there are 3 students who can receive these trophies.
Step 3: For each trophy, we can choose any of the 3 students to receive it.
Step 4: Since there are 5 trophies, and each trophy can go to any of the 3 students, we multiply the choices.
Step 5: The number of choices for each trophy is 3, and we have 5 trophies, so we calculate 3 multiplied by itself 5 times (3^5).
Step 6: Calculate 3^5, which equals 243.
Step 7: Conclude that there are 243 different ways to award the 5 trophies to the 3 students.
Combinatorics – The question tests the understanding of distributing distinct items (trophies) to distinct recipients (students) where each item can go to any recipient.
Exponential Counting – The solution involves using the principle of counting where each trophy can be awarded to any of the 3 students, leading to an exponential calculation.
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