A square is divided into 9 identical smaller squares. Now, In how many ways can 5 different balls be placed in them such that every cell has at least 1 ball ?
The mentioned query can have 2 case
Case I:
If one row contains 3 balls and the other two rows contain 1 ball each
Then, number of ways of arrangement = 3C1 × (3C3 × 3C1 × 3C1) = 27 ways
Case II:
If one row contains 1 ball and the other two rows contain 2 balls each.
Then, number of arrangements = 3C1 × (3C2 × 3C2 × 3C1) = 81.
Hence, total number of arrangements = 27 + 81 = 108