# How many three-digit numbers are there with no digit repeated?

Question:

How many three-digit numbers are there with no digit repeated?

Solution:

The thousand's place cannot be zero.

∴ Number of ways of selecting the thousand's digit = 9

Number of ways of selecting the ten's digit = 9 ( as repetition of digits is not allowed and one digit has already been used in the thousand's place)

Similarly, number of ways of selecting the unit's digit = 8 (as two digits have been used for the thousand's and the ten's places)

$\therefore$ Total three digit number that can be formed $=9 \times 9 \times 8=648$