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.

Suppose all the balls and all the boxes are also identical. Then in how many ways can all these balls be distributed among these boxes?

• A. 12
• B. 13
• C. 16
• D. 255

Answer 1

The correct option is B 13

Possible ways of distribution are as follows:
(i) (7) (ii) (6+1) (iii) (5+2) (iv) (4+3) (v) (5+1+1) (vi) (4+2+1) (vii) (3+2+2) (viii) (3+3+1) (ix) (4+1+1+1) (x) (3+2+1+1) (xi) (2+2+2+1) (xii) (3+1+1+1+1) (xiii) (2+2+1+1+1)
Hence total number of ways of distribution = 13.