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A school awards 3 medals for first place, 2 for second place, and 1 for third pl

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Question: A school awards 3 medals for first place, 2 for second place, and 1 for third place. If there are 5 participants, how many different ways can the medals be awarded?

Options:

  1. 60
  2. 30
  3. 20
  4. 10

Correct Answer: 60

Solution: 

The number of ways to award the medals is calculated using permutations: 5P3 = 5!/(5-3)! = 5*4*3 = 60.

A school awards 3 medals for first place, 2 for second place, and 1 for third pl

Practice Questions

Q1
A school awards 3 medals for first place, 2 for second place, and 1 for third place. If there are 5 participants, how many different ways can the medals be awarded?
  1. 60
  2. 30
  3. 20
  4. 10

Questions & Step-by-Step Solutions

A school awards 3 medals for first place, 2 for second place, and 1 for third place. If there are 5 participants, how many different ways can the medals be awarded?
  • Step 1: Understand that we have 5 participants and we need to award medals for 1st, 2nd, and 3rd places.
  • Step 2: Recognize that we are interested in the order of the participants because 1st, 2nd, and 3rd places are different.
  • Step 3: Use the concept of permutations to find the number of ways to arrange the top 3 participants out of 5.
  • Step 4: The formula for permutations is nPr = n! / (n - r)!, where n is the total number of participants and r is the number of positions to fill.
  • Step 5: In this case, n = 5 (participants) and r = 3 (medals), 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 / 2 = 60.
  • Step 9: Conclude that there are 60 different ways to award the medals.
  • Permutations – The arrangement of items in a specific order, used here to determine the different ways to award medals to participants.
  • Factorials – A mathematical operation that multiplies a number by all positive integers less than it, essential for calculating permutations.
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