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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## A company plans to assign identification numbers to its tagged by: AAPL ##### This topic has 3 expert replies and 0 member replies ### Top Member ## A company plans to assign identification numbers to its ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult 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. ### GMAT/MBA Expert GMAT Instructor Joined 08 Dec 2008 Posted: 12649 messages Followed by: 1245 members Upvotes: 5254 GMAT Score: 770 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-counting/video/775 You can also watch a demonstration of the FCP in action: https://www.gmatprepnow.com/module/gmat-counting/video/776 Then you can try solving the following questions: EASY - https://www.beatthegmat.com/what-should-be-the-answer-t267256.html - https://www.beatthegmat.com/counting-problem-company-recruitment-t244302.html - https://www.beatthegmat.com/picking-a-5-digit-code-with-an-odd-middle-digit-t273110.html - https://www.beatthegmat.com/permutation-combination-simple-one-t257412.html - https://www.beatthegmat.com/simple-one-t270061.html MEDIUM - https://www.beatthegmat.com/combinatorics-solution-explanation-t273194.html - https://www.beatthegmat.com/arabian-horses-good-one-t150703.html - https://www.beatthegmat.com/sub-sets-probability-t273337.html - https://www.beatthegmat.com/combinatorics-problem-t273180.html - https://www.beatthegmat.com/digits-numbers-t270127.html - https://www.beatthegmat.com/doubt-on-separator-method-t271047.html - https://www.beatthegmat.com/combinatorics-problem-t267079.html DIFFICULT - https://www.beatthegmat.com/wonderful-p-c-ques-t271001.html - https://www.beatthegmat.com/permutation-and-combination-t273915.html - https://www.beatthegmat.com/permutation-t122873.html - https://www.beatthegmat.com/no-two-ladies-sit-together-t275661.html - https://www.beatthegmat.com/combinations-t123249.html Cheers, Brent _________________ Brent Hanneson – Creator of GMATPrepNow.com Use our video course along with Sign up for our free Question of the Day emails And check out all of our free resources GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMAT’s FREE 60-Day Study Guide and reach your target score in 2 months! ### GMAT/MBA Expert GMAT Instructor Joined 09 Oct 2010 Posted: 1273 messages Followed by: 29 members Upvotes: 59 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. _________________ Fabio Skilnik :: GMATH method creator ( Math for the GMAT) English-speakers :: https://www.gmath.net Portuguese-speakers :: https://www.gmath.com.br ### GMAT/MBA Expert GMAT Instructor Joined 25 Apr 2015 Posted: 2006 messages Followed by: 14 members Upvotes: 43 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 _________________ Scott Woodbury-Stewart Founder and CEO • FREE GMAT Exam Know how you'd score today for$0

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