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A school awards 3 different prizes to 5 students. If each student can win only o

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Question: A school awards 3 different prizes to 5 students. If each student can win only one prize, how many different ways can the prizes be awarded?

Options:

  1. 60
  2. 120
  3. 30
  4. 90

Correct Answer: 120

Solution: 

The number of ways to award the prizes is calculated as 5P3 = 5! / (5-3)! = 5 * 4 * 3 = 60.

A school awards 3 different prizes to 5 students. If each student can win only o

Practice Questions

Q1
A school awards 3 different prizes to 5 students. If each student can win only one prize, how many different ways can the prizes be awarded?
  1. 60
  2. 120
  3. 30
  4. 90

Questions & Step-by-Step Solutions

A school awards 3 different prizes to 5 students. If each student can win only one prize, how many different ways can the prizes be awarded?
  • Step 1: Understand that we have 5 students and we want to award 3 different prizes.
  • Step 2: Realize that each student can only win one prize, so we need to choose 3 students from the 5 to receive the prizes.
  • Step 3: The order in which we award the prizes matters because they are different prizes.
  • Step 4: Use the formula for permutations, which is represented as 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), so we calculate 5P3.
  • Step 6: Plug the numbers into the formula: 5P3 = 5! / (5 - 3)! = 5! / 2!.
  • Step 7: Calculate 5! (which is 5 x 4 x 3 x 2 x 1 = 120) and 2! (which is 2 x 1 = 2).
  • Step 8: Now divide 120 by 2 to get 60.
  • Step 9: Conclude that there are 60 different ways to award the prizes.
  • Permutations – The arrangement of a subset of items from a larger set, where the order of selection matters.
  • Factorial – The product of all positive integers up to a given number, used in calculating permutations.
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