Question

Seven different gifts are to be distributed among 10 children.

How many distinct results are possible if no child is to receive more than one gift?

Answer 1

There are 120 distinct ways to distribute 7 different gifts among 10 children without any child receiving more than one gift.

Step-by-step explanation:

To distribute 7 different gifts among 10 children without giving any child more than one gift, we can use the concept of combinations. The formula for the number of combinations is nCr, where n is the total number of items and r is the number of items to be chosen. In this case, we want to choose 7 gifts out of 10 children, so the number of combinations is 10C7.

Using the formula nCr = n! / (r!(n-r)!), we can calculate:

10C7 = 10! / (7!(10-7)!) = 10! / (7!3!) = (10 * 9 * 8) / (3 * 2 * 1) = 120

Therefore, there are 120 distinct ways to distribute 7 different gifts among 10 children without any child receiving more than one gift.