Problem Solving

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

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!