Question

There are 10 people who can win 4 different prizes. The number of ways they can win them is:

A) 1,680
B) 2,520
C) 5040
D) 10,080

Answer 1

To find the number of ways that 10 people can win 4 different prizes, you can use the concept of permutations. Using the formula for permutations, the number of ways is 5,040.

Step-by-step explanation:

To find the number of ways that 10 people can win 4 different prizes, we can use the concept of permutations. Permutations calculate the number of ways to arrange items when the order matters. In this case, each person can win a different prize, so the order does matter. We can use the formula for permutations:

nPr = n! / (n - r)!

Where n is the total number of items (10 in this case) and r is the number of items to be chosen (4 in this case).

Using the formula, we can calculate:

nPr = 10! / (10 - 4)! = 10! / 6! = (10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1) / (6 * 5 * 4 * 3 * 2 * 1) = 10 * 9 * 8 * 7 = 5,040.

Therefore, the number of ways that 10 people can win 4 different prizes is 5,040.