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

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

$=\frac{5 !}{(5-3) !}$

$=\frac{5 !}{2 !}$

$=\frac{5 \times 4 \times 3 \times 2 !}{2 !}$

$=5 \times 4 \times 3$

= 60