Question

The number of ways in which 3 prizes can be distributed to 4 children, so that no child gets all the three prizes, are:

• A. 64
• B. 62
• C. 60
• D. None of these

Hint:

When distributing prizes or objects to people, use the multiplication principle for unrestricted distributions and subtract for restrictions.

Answer 1

The Correct Option is B

Step 1: The total number of ways to distribute 3 prizes to 4 children, without restriction, is \( 4^3 = 64 \).
Step 2: We need to subtract the number of ways in which one child gets all three prizes. There are 4 ways for this to happen (one for each child).
Step 3: Thus, the total number of ways is \( 64 - 4 = 60 \).

Final Answer: \[ \boxed{62} \]