Question

A company plans to assign identification numbers to its employees. Each number is to consist of four different digits from 0 to 9, inclusive, except that the first digit cannot be 0. How many different identification numbers are possible?

Answer 1

The answer is 4536.

Explanation:

Each number is to consist of four different digits(no repetition) from 0 to 9, except that the first digit cannot be 0.

Total numerals from 0 to 9 = 10

For 1st place you have 9 options for 1st digit (0 is not selected here).

For the 2nd place you again have 9 numbers (0 is available but 1 digit less from 10 as it is already selected in first place) so, you get 9c1 ways = 9

For the 3rd place you have 8c1 ways = 8

For the 4th place you have 7c1 ways = 7

Total number of identification numbers are :
`9*9*8*7=4536`

Therefore, there are 4536 different identification numbers.