Question

Find n(S) of the following random experiment.

5 letters are to be placed into 5 envelopes such that no envelope is empty.

Answer 1

The first letter can be placed into any of the 5 envelopes in 5 different ways

Since no envelope should be empty, the second letter can be placed into any of the 4 remaining envelopes in 4 different ways.

Similarly, the remaining 3 letters can be placed in envelopes in 3, 2, 1 ways respectively

∴ n(S) = 5 × 4 × 3 × 2 × 1

= 120