In how many ways can 3 prizes be distributed among 5 students? (2021)

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Question: In how many ways can 3 prizes be distributed among 5 students? (2021)

Options:

Correct Answer: 120

Exam Year: 2021

Solution:

The number of ways to distribute 3 prizes to 5 students is 5P3 = 60.

In how many ways can 3 prizes be distributed among 5 students? (2021)

In how many ways can 3 prizes be distributed among 5 students? (2021)

Step 1: Understand that we have 3 prizes to give away.
Step 2: Recognize that there are 5 students who can receive these prizes.
Step 3: Realize that the order in which we give the prizes matters (since each prize is distinct).
Step 4: Use the formula for permutations, which is nPr = n! / (n - r)!, where n is the total number of students and r is the number of prizes.
Step 5: In this case, n = 5 (students) and r = 3 (prizes).
Step 6: Calculate 5P3 using the formula: 5P3 = 5! / (5 - 3)! = 5! / 2!.
Step 7: Calculate 5! = 5 × 4 × 3 × 2 × 1 = 120.
Step 8: Calculate 2! = 2 × 1 = 2.
Step 9: Now divide: 120 / 2 = 60.
Step 10: Conclude that there are 60 different ways to distribute the 3 prizes among the 5 students.

Permutations – The question tests the understanding of permutations, specifically how to calculate the number of ways to arrange a subset of items (prizes) from a larger set (students).
Combinatorial Counting – It also involves combinatorial counting principles, where the order of distribution matters since each prize is distinct.