How many ways can 10 different trophies be awarded to 3 different winners?

How many ways can 10 different trophies be awarded to 3 different winners?

Correct Answer: 720

Step 1: Understand that we have 10 different trophies and we want to award them to 3 different winners.
Step 2: Recognize that the order in which we award the trophies matters because each trophy is different.
Step 3: Use the formula for permutations, which is P(n, r) = n! / (n - r)!, where n is the total number of items (trophies) and r is the number of items to choose (winners).
Step 4: In this case, n = 10 (trophies) and r = 3 (winners).
Step 5: Plug the values into the formula: P(10, 3) = 10! / (10 - 3)!.
Step 6: Calculate (10 - 3) which is 7, so we have P(10, 3) = 10! / 7!.
Step 7: Simplify 10! / 7! to 10 × 9 × 8 because the 7! cancels out the 7! in the denominator.
Step 8: Calculate 10 × 9 = 90, and then 90 × 8 = 720.
Step 9: Conclude that there are 720 different ways to award the 10 trophies to 3 winners.

No concepts available.