How many ways can 3 different gifts be given to 5 children if each child can rec

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Question: How many ways can 3 different gifts be given to 5 children if each child can receive more than one gift? (2022)

Options:

Correct Answer: 243

Exam Year: 2022

Solution:

Each gift can go to any of the 5 children, so the total ways = 5^3 = 125.

How many ways can 3 different gifts be given to 5 children if each child can receive more than one gift? (2022)

How many ways can 3 different gifts be given to 5 children if each child can receive more than one gift? (2022)

Step 1: Identify the number of gifts. In this case, there are 3 different gifts.
Step 2: Identify the number of children. Here, there are 5 children.
Step 3: Understand that each gift can be given to any of the 5 children. This means for each gift, there are 5 choices.
Step 4: Calculate the total number of ways to distribute the gifts. Since there are 3 gifts and each gift has 5 choices, you multiply the choices together: 5 (for the first gift) * 5 (for the second gift) * 5 (for the third gift).
Step 5: This can be simplified using exponents. Since you have 3 gifts, you can write it as 5^3.
Step 6: Calculate 5^3, which equals 125. This is the total number of ways to give the gifts.

Combinatorics – The problem involves counting the number of ways to distribute distinct items (gifts) to distinct recipients (children) with the possibility of multiple items going to the same recipient.
Exponential Counting – Each gift can be given to any of the 5 children independently, leading to the use of exponentiation to calculate the total combinations.