How many ways can 3 prizes be awarded to 10 students if no student can win more

How many ways can 3 prizes be awarded to 10 students if no student can win more than one prize?

How many ways can 3 prizes be awarded to 10 students if no student can win more than one prize?

Step 1: Understand that we have 10 students and we want to award 3 prizes.
Step 2: Realize that each prize can only be awarded to a different student (no student can win more than one prize).
Step 3: The first prize can be awarded to any of the 10 students, so there are 10 choices for the first prize.
Step 4: After awarding the first prize, only 9 students are left for the second prize, so there are 9 choices for the second prize.
Step 5: After awarding the second prize, only 8 students are left for the third prize, so there are 8 choices for the third prize.
Step 6: To find the total number of ways to award the prizes, multiply the number of choices together: 10 choices for the first prize × 9 choices for the second prize × 8 choices for the third prize.
Step 7: Calculate: 10 × 9 × 8 = 720.
Step 8: Therefore, the total number of ways to award 3 prizes to 10 students is 720.

Permutations – The problem involves calculating the number of ways to arrange a subset of items (prizes) from a larger set (students) where the order matters and no item can be repeated.