Question

How many three-digit numbers are there, with distinct digits, with each digit odd?

Answer 1

The odd digits are 1, 3, 5, 7 and 9.

Required number of ways = Number of arrangements of five digits ( 1, 3, 5, 7 and 9), taken three at a time = ⁵P₃
$$\begin{gathered} =\frac{5!}{(5-3)!} \\ =\frac{5!}{2!} \\ =\frac{5\times 4\times 3\times 2!}{2!} \\ =5\times 4\times 3 \\ =60 \end{gathered}$$