Question

In how many ways can 5 prizes be distributed among 4 boys when every boy can take one or more prizes?

• A. 1024
• B. 625
• C. 120
• D. 600

Hint:

Use the stars and bars method for distributing identical items among distinct groups.

Answer 1

The Correct Option is A

Step 1: Use the stars and bars method.
The stars and bars method is used to calculate the number of ways of distributing \( n \) identical items among \( r \) groups. The number of ways is given by \( r^n \). In this case, there are 4 boys and 5 prizes, so the total number of ways is \( 4^5 = 1024 \).
Thus, the correct answer is (1).