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

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 = [tex]9\times9\times8\times7=4536[/tex]

The number of different identification numbers are possible is 4536.

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

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

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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