A company plans to assign identification numbers to its employees. Each number is to consist of four different digits

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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


OA B

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Since 0 can't be the first digit there are

9 choices for the first digit .

For the second digit there are also 9 choices since 0 can be used.

Third digit then

8 choices. And fourth digit

7 choices.

So the total is 9*9*8*7.

Rather than multiplying this out, we can see that the 9*9 will leave a 1 as the first digit, which multiplied by 8 leaves 8 as the first digit, then multiplied by 7 leaves

6 as the first digit.

Only B satisfies

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BTGmoderatorDC wrote:
Wed Nov 02, 2022 11:55 pm
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

Source: GMAT Prep
There are 9 choices for the first digit (1 through 9, inclusive). The second digit can be any of the 10 digits (0 through 9, inclusive) EXCEPT it can’t repeat the first digit; thus, there are 9 options for the second digit. The third digit can’t repeat either of the first two digits, so there are 8 options. Similarly, the fourth digit can’t repeat any of the first 3 digits, so there are 7 options. Thus, the total number of options is 9 x 9 x 8 x 7 = 4,536.

Answer: B

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