Question

How many different numbers of three digits can be formed with the digits 1, 2, 3, 4, 5, no digit is being repeated?

Answer 1

The unit’s place can be filled with either of these 5 digits and so the unit’s place can be filled in 5 ways. The ten’s place can be filled in 4 ways corresponding to each way of filling up the unit’s place, for we can have any digit here except the one used in the unit’s place. Similarly, the hundredth’s place can be filled in 3 ways as here we have any of the remaining three digits. Therefore, there are 5 × 4 × 3 = 60 ways of forming a number of three digits with the five given digits.