A sports event awards medals to the top 3 finishers. If there are 12 participant

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Question: A sports event awards medals to the top 3 finishers. If there are 12 participants, how many different ways can the medals be awarded?

Options:

Correct Answer: 1320

Solution:

The number of ways to award medals is calculated using permutations: P(12, 3) = 12! / (12-3)! = 12 * 11 * 10 = 1320.

A sports event awards medals to the top 3 finishers. If there are 12 participants, how many different ways can the medals be awarded?

A sports event awards medals to the top 3 finishers. If there are 12 participants, how many different ways can the medals be awarded?

Step 1: Understand that we need to award medals to the top 3 finishers out of 12 participants.
Step 2: Recognize that the order in which the medals are awarded matters (1st, 2nd, and 3rd place are different).
Step 3: Use the concept of permutations because we are selecting and arranging 3 participants from a group of 12.
Step 4: The formula for permutations is P(n, r) = 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 = 12 (participants) and r = 3 (medals). So we calculate P(12, 3).
Step 6: Substitute the values into the formula: P(12, 3) = 12! / (12 - 3)! = 12! / 9!.
Step 7: Simplify the factorials: 12! = 12 × 11 × 10 × 9! and 9! cancels out, leaving us with 12 × 11 × 10.
Step 8: Calculate the result: 12 × 11 = 132, then 132 × 10 = 1320.
Step 9: Conclude that there are 1320 different ways to award the medals.

Permutations – The arrangement of items where the order matters, used here to determine the different ways to award medals to the top 3 finishers.