Question

4 letters are to be posted in 4 post boxes. If any number of letters can be posted in any of the 4 post boxes, what is the probability that each box contains only one letter?

Answer 1

There are 4 letters and 4 post boxes.

Since any number of letters can be posted in all 4 post boxes, so each letter can be posted in 4 different ways.

∴ n(S) = 4 x 4 x 4 x 4

Let event A: Each box contains only one letter.

∴ 1^st letter can be posted in 4 different ways.

Since each box contains only one letter,

2^nd letter can be posted in 3 different ways.

Similarly, 3^rd and 4^th letters can be posted in 2 different ways and 1 way respectively.

∴ n(A) = 4 x 3 x 2 x 1

∴ P(A) = `("n"("A"))/("n"("S"))`

= `(4 xx 3 xx 2 xx 1)/(4 xx 4 xx 4 xx 4)`

= `3/32`.