In how many ways can 3 prizes be awarded to 5 students? (2021)

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

Options:

Correct Answer: 120

Exam Year: 2021

Solution:

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

In how many ways can 3 prizes be awarded to 5 students? (2021)

In how many ways can 3 prizes be awarded to 5 students? (2021)

Step 1: Understand that we have 5 students and we want to award 3 prizes.
Step 2: Recognize that the order in which the prizes are awarded matters (1st prize, 2nd prize, 3rd prize).
Step 3: Use the formula for permutations since we are selecting and arranging 3 prizes from 5 students. The formula is nPr = n! / (n - r)!, where n is the total number of students and r is the number of prizes.
Step 4: Plug in the values: n = 5 (students) and r = 3 (prizes). So we calculate 5P3 = 5! / (5 - 3)!.
Step 5: Calculate 5! (which is 5 x 4 x 3 x 2 x 1 = 120) and (5 - 3)! = 2! (which is 2 x 1 = 2).
Step 6: Now divide: 120 / 2 = 60.
Step 7: Conclude that there are 60 different ways to award the 3 prizes to 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 selection matters since the prizes are distinct.