How many 3-digit numbers are there, with distinct digits, with each digit odd?
Since each digit of the 3-digit number is odd, the available digits are $1, \; 3, \; 5, \; 7, \; 9$
i.e. $\;$ Number of digits available $= 5$ digits
A 3-digit number can be selected from the 5 digits in
${^{5}}{P}_{3} = \dfrac{5!}{\left(5 - 3\right)!} = \dfrac{5!}{2!} = \dfrac{5 \times 4 \times 3 \times 2!}{2!} = 60$ ways
$\therefore \;$ Number of possible 3-digit numbers, with distinct odd digits is $60$.