A company plans to assign identification numbers to its

Question

GMAT Prep 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.

Brent@GMATPrepNow · Answer

AAPL wrote:GMAT Prep 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. Take the task of creating the identification numbers and break it into stages. Stage 1: Select the first digit of the identification number The first digit can be 1, 2, 3, 4, 5, 6, 7, 8, or 9 So, we can complete stage 1 in 9 ways Stage 2: Select the second digit of the identification number The second digit can be any digit from 0 to 9 OTHER THAN the digit chosen in stage 1 So, we can complete stage 2 in 9 ways . Stage 3: Select the third digit of the identification number The third digit can be any digit from 0 to 9 OTHER THAN the 2 digits digit chosen in stages 1 and 2 So we can complete this stage in 8 ways. Stage 4: Select the fourth digit of the identification number The third digit can be any digit from 0 to 9 OTHER THAN the 3 digits digit chosen earlier So we can complete this stage in 7 ways. By the Fundamental Counting Principle (FCP), we can complete all 4 stages (and thus create all of the identification numbers) in (9)(9)(8)(7) ways (= 4,536 ways) Answer: B -------------------------- Note: the FCP can be used to solve the MAJORITY of counting questions on the GMAT. For more information about the FCP, watch our free video: https://www.gmatprepnow.com/module/gmat ... /video/775 You can also watch a demonstration of the FCP in action: https://www.gmatprepnow.com/module/gmat ... /video/776 Then you can try solving the following questions: EASY - https://www.beatthegmat.com/what-should ... 67256.html - https://www.beatthegmat.com/counting-pr ... 44302.html - https://www.beatthegmat.com/picking-a-5 ... 73110.html - https://www.beatthegmat.com/permutation ... 57412.html - https://www.beatthegmat.com/simple-one-t270061.html MEDIUM - https://www.beatthegmat.com/combinatori ... 73194.html - https://www.beatthegmat.com/arabian-hor ... 50703.html - https://www.beatthegmat.com/sub-sets-pr ... 73337.html - https://www.beatthegmat.com/combinatori ... 73180.html - https://www.beatthegmat.com/digits-numbers-t270127.html - https://www.beatthegmat.com/doubt-on-se ... 71047.html - https://www.beatthegmat.com/combinatori ... 67079.html DIFFICULT - https://www.beatthegmat.com/wonderful-p ... 71001.html - https://www.beatthegmat.com/permutation ... 73915.html - https://www.beatthegmat.com/permutation-t122873.html - https://www.beatthegmat.com/no-two-ladi ... 75661.html - https://www.beatthegmat.com/combinations-t123249.html Cheers, Brent

fskilnik@GMATH · Answer

AAPL wrote:GMAT Prep 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 Immediate application of the Multiplicative Principle: $$\begin{array}{*{20}{c}} {\underline {{\text{not}}\,\,0} } \ 9 \end{array}\begin{array}{*{20}{c}} {\underline {{\text{nr}}} } \ 9 \end{array}\begin{array}{*{20}{c}} {\underline {{\text{nr}}} } \ 8 \end{array}\begin{array}{*{20}{c}} {\underline {{\text{nr}}} } \ 7 \end{array}\,\,\,\,\,\mathop \Rightarrow \limits^{{\text{Multipl}}{\text{.}}\,{\text{Principle}}} \,\,\,\,? = {9^2} \cdot 8 \cdot 7\,\,\,\,\,\,\,\,\,\,\left[ {nr = {\text{no}}\,\,{\text{repetition}}} \right]$$ $$\left\langle ? \right\rangle = \left\langle {{9^2}} \right\rangle \cdot \left\langle {8 \cdot 7} \right\rangle = 1 \cdot 6 = 6\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left[ {\left\langle N \right\rangle = {\text{units}}\,\,{\text{digit}}\,\,{\text{of}}\,\,N} \right]$$ Just one alternative choice with unit´s digit equal to the correct one... we are done! This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio.

Scott@TargetTestPrep · Answer

AAPL wrote:GMAT Prep 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 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

Choose how you want to prepare

Get Ready for GMAT Test Day Faster with Live Online Classes

Target Test Prep EA OnDemand

Target Test Prep GMAT OnDemand

A company plans to assign identification numbers to its

GMAT/MBA Expert

A company plans to assign identification numbers to its

GMAT/MBA Expert

Chicago Booth

GMAT Course Reviews

Admissions Consulting Reviews

FREE GMAT PREP RESOURCES

GMAT PREP DEAL TRACKER