In how many ways can 4 different gifts be distributed among 3 children?

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Question: In how many ways can 4 different gifts be distributed among 3 children?

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?

In how many ways can 4 different gifts be distributed among 3 children?

Step 1: Identify the number of gifts. We have 4 different gifts.
Step 2: Identify the number of children. We have 3 children.
Step 3: Understand that each gift can be given to any of the 3 children.
Step 4: For the first gift, there are 3 choices (Child 1, Child 2, or Child 3).
Step 5: For the second gift, there are also 3 choices (Child 1, Child 2, or Child 3).
Step 6: Repeat this for the third gift, which also has 3 choices.
Step 7: Do the same for the fourth gift, which again has 3 choices.
Step 8: Since the choices for each gift are independent, multiply the number of choices together: 3 (for the first gift) * 3 (for the second gift) * 3 (for the third gift) * 3 (for the fourth gift).
Step 9: This can be written as 3^4 (3 raised to the power of 4).
Step 10: Calculate 3^4, which equals 81.
Step 11: Conclude that there are 81 different ways to distribute the 4 gifts among the 3 children.

Combinatorics – The problem involves distributing distinct items (gifts) to distinct recipients (children), which is a basic combinatorial problem.
Exponential Counting – Each gift has multiple choices (3 children), leading to an exponential counting method where the total number of distributions is calculated as the number of choices raised to the number of items.