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

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by BTGmoderatorDC » Sat Feb 26, 2022 6:29 pm

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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

Source: GMAT Prep
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Re: A company plans to assign identification numbers to its employees. Each number is to consist of four different digit

by swerve » Sun Feb 27, 2022 6:50 am
BTGmoderatorDC wrote: ↑
Sat Feb 26, 2022 6:29 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
Since we have to form \(4\) digit number with the 1st digit non-zero and all different digits.
It can be formed in the following way

\(1\)st digit\(\Rightarrow \, 9\) ways \((1 to 9)\)
\(2\)nd digit \(\Rightarrow\, 9\) ways \((0\) to \(9\) excluding \(1\)st digit\()\)
\(3\)rd digit \(\Rightarrow \, 8\) ways \(( 0\) to \(9\) excluding \(1\)st and \(2\)nd digit\()\)
\(4\)th digit \(\Rightarrow\, 7\) ways \((0\) to \(9\) excluding \(1\)st, \(2\)nd and \(3\)rd digit\()\)

So total no. of ways \(= 9\cdot 9 \cdot 8 \cdot 7 = 4536\) ways

Hope this helps!
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