Problem Solving

GMAT Prep

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?

A. 3,024
B. 4,536
C. 5,040
D. 9,000
E. 10,000

OA B

1st digit can be anything from 1 to 9, So 9 possible digits.
2nd can be anything from 0 to 9 but not the one used as the 1st digit, so again 10- 1 = 9 possible values.
3rd can be anything from 0 to 9 except the two digits used as the 1st and the 2nd digit, so 10-2 = 8 possible values.
4th can be anything from 0 to 9 except the 3 digits used as the 1st, 2nd and 3rd digit, so 10-3 = 7.

Hence total possibilities = 9x9x8x7 = 4536.

Regards!