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?
(A) 3,024
(B) 4,536
(C) 5,040
(D) 9,000
(E) 10,000

Answer 1

Answer: B) 4536

Step-by-step explanation:

Given : 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.

i.e. The number of choices for first digit = 9   (Total digits = 1)

The number of choices for second digit = 9  (one get fixed in first place and 0 can be used)

Similarly, The number of choices for third digit = 8  ( two got fixed on 1st and second place)

The number of choices for fourth digit = 7  (Three places are fixed.)

By Fundamental counting principle ,

The number of different identification numbers are possible = $9\times9\times8\times7=4536$

The number of different identification numbers are possible is 4536.

Therefore , the correct answer is (B) 4,536.