How many three-digit numbers are there, with distinct digits, with each digit odd?
Given: The odd digits are: 1, 3, 5, 7 and 9.
∴ The total number of odd-digits = 5
To find: Total number of three-digit numbers, with distinct digits, with each digit odd like 135 or 159 etc.
Formula used:
Number of arrangements of n things taken r at a time = P(n, r)
∴The total number of ways in which this can be done
= the number of arrangements of 5 things taken 3 at a time
= P(5, 3)
= 5 × 4 × 3
= 60
Hence, total number of three-digit numbers, with distinct digits, with each digit odd are 60