In how many ways can 4 different gifts be distributed among 3 children if each c

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Question: In how many ways can 4 different gifts be distributed among 3 children if each child can receive any number of gifts?

Options:

Correct Answer: 81

Solution:

Each gift can go to any of the 3 children, so the total ways are 3^4 = 81.

In how many ways can 4 different gifts be distributed among 3 children if each child can receive any number of gifts?

In how many ways can 4 different gifts be distributed among 3 children if each child can receive any number of gifts?

Step 1: Identify the number of gifts. In this case, there are 4 different gifts.
Step 2: Identify the number of children. Here, there are 3 children.
Step 3: Understand that each gift can be given to any of the 3 children. This means for each gift, there are 3 choices.
Step 4: Calculate the total number of ways to distribute the gifts. Since there are 4 gifts and each gift has 3 choices, you multiply the choices for each gift: 3 choices for the first gift, 3 choices for the second gift, 3 choices for the third gift, and 3 choices for the fourth gift.
Step 5: This can be expressed mathematically as 3^4 (3 raised to the power of 4).
Step 6: Calculate 3^4, which equals 81. This means there are 81 different ways to distribute the 4 gifts among the 3 children.

Combinatorial Distribution – The problem tests the understanding of distributing distinct items (gifts) to distinct recipients (children) where each recipient can receive multiple items.