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
A company plans to assign identification numbers to its employees. Each number is to consist of four different digits
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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
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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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.BTGmoderatorDC wrote: ↑Wed Nov 02, 2022 11:55 pmA 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
Answer: B
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