Question

There are 5 different boxes and 7 different balls. All the 7 balls are to be distributed among the 5 boxes placed in a row so that any box can receive any number of balls.

In how many ways can these balls be distributed among these boxes if ball 2 can be put into either box 2 or box 4?

• A. 12360
• B. 31250
• C. 13490
• D. 31526

Answer 1

The correct option is B 31250

Ball 2 can be distributed between 2 boxes (viz, box 2 and box 4) in 2 ways.
Now, the remaining 6 balls can be distributed among any of the 5 boxes in $5^6$ ways.
Hence, the required number of ways $=2\times 5^6$ ways
= 31250 ways