Let´s assume that we don´t have to use all digits 1,2 and 3 to form the number. We define $X,Y,Z\in \{1,2,3 \}$ Show
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Case 1: Two different groups of digits, where each group consists of one kind of number.: $XXXYY$ These sequence can be arranged in $\frac{5!}{3!\cdot 2!}=\frac{120}{12}=10$ ways. $X$ and $Y$ can have the following combinations: $(1,2);(2;1);(1,3);(3,1);(2,3);(3,2)$ Thus for case 1 we have $6\cdot 10=60$ ways. Case 2: Three different groups of digits where each group consists of one kind number and one group has 3 digits: $XXXYZ$. This sequence can be arranged in $\frac{5!}{3!\cdot 1!\cdot 1!}=\frac{120}{6}=20$ ways. $X,Y,Z$ can have $3$ combinations and for case 2 there exists $60$ ways. Finally we can say that $120$ five digit numbers can be formed using digits 1,2,3 with exactly one digit repeating 3 times. How many 5-digit prime numbers can be formed using the digits 1, 2, 3, 4, 5 if the repetition of digits is not allowed?This question was previously asked in NDA (Held On: 18 Apr 2021) Maths Previous Year paper View all NDA Papers >
Answer (Detailed Solution Below)Option 4 : 0 Free Electric charges and coulomb's law (Basic) 10 Questions 10 Marks 10 Mins Concept: Prime number: Prime number are those which are divisible by itself and 1. Calculation: Not a single five-digit prime number can be formed using the digits 1, 2, 3, 4, 5(without repetition). This is because if one adds the digits, the result obtained will be = 1 + 2 + 3 + 4 + 5 = 15 which is divisible by 3. Hence, any number obtained as a permutation of these 5 digits will be at least divisible by 3 and cannot be a prime number. Last updated on Sep 16, 2022 Union Public Service Commission (UPSC) has released the admit card for the UPSC NDA II 2022 exam. The Prelims exam of NDA II 2022 is scheduled to be held on 4th September 2022. The last date to download the admit card will be 4th September 2022. A total number of 400 vacancies are released for the UPSC NDA II 2022 exam. The selection process for the exam includes a Written Exam and SSB Interview. Candidates who get successful selection under UPSC NDA II will get a salary range between Rs. 15,600 to Rs. 39,100. Know the UPSC NDA preparation strategy here. With hundreds of Questions based on Permutations and Combinations, we help you gain expertise on Mathematics. All for free. Explore Testbook Learn to attain the subject expertise with us. The sum of all five-digit numbers that can be formed using the digits 1, 2, 3, 4, 5 when repetition of digits is not allowed, is(1) 366000 (2) 660000 (3) 360000 (4) 3999960 Answer: (4) 3999960 Solution: Sum of all 5- digit numbers by using 1,2,3,4,5 without repetition= (Sum of all digits) (n-1)! (10n-1/10-1) = (1+2+3+4+5)4!(105-1/10-1) = 15 x 4 x 3 x 2 x (105-1)/(10-1) = 15 x 12 x 2 (100000-1)/9 = 40 x 99999 = 399960 GMAT Club Daily PrepThank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.Customized we will pick new questions that match your level based on your Timer History Track every week, we’ll send you an estimated GMAT score based on your performance Practice we will pick new questions that match your level based on your Timer History Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.Hello Guest!It appears that you are browsing the GMAT Club forum unregistered! Signing up is free, quick, and confidential. Join 700,000+ members and get the full benefits of GMAT ClubRegistration gives you:
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Yale Moderator Joined: 05 May 2019 Posts: 171 GPA: 3 How many numbers can be formed from 1, 2, 3, 4, 5 (without repetition) [#permalink] Updated on: 20 Jan 2020, 05:3700:00 Question Stats: 61% (02:07) correct 39% (02:19) wrong based on 109 sessionsHide Show timer StatisticsHow many five digit numbers can be formed from 1, 2, 3, 4, 5 (without repetition), when the digit at the unit’s place must be greater than that in the ten’s place? (a) \(54\) Originally posted by sharathnair14 on 10 Jan 2020, 09:38. GMAT Tutor Joined: 05 Apr 2011 Status:Tutor - BrushMyQuant Posts: 1132 Location: India Concentration: Finance, Marketing GPA: 3 WE:Information Technology (Computer Software) How many numbers can be formed from 1, 2, 3, 4, 5 (without repetition) [#permalink] Updated on: 15 Jul 2020, 09:45 Total Number of Numbers which can be formed by numbers 1,2,3,4,5 (without repeating digitsi) = 5*4*3*2*! = 5! = 120. Example: Let's say we have three digits 1,2,3. Total number of numbers without repeating digits = 3*2*1=6 So total Number of cases = 120/2 = 60 Originally posted by BrushMyQuant on 11 Jan 2020, 08:59. Manager Joined: 13 Aug 2018 Posts: 60 Re: How many numbers can be formed from 1, 2, 3, 4, 5 (without repetition) [#permalink] 19 Jan 2020, 01:24sharathnair14 wrote: How many numbers can be formed from 1, 2, 3, 4, 5 (without repetition), when the digit at the unit’s place must be greater than that in the ten’s place? (a) \(54\) unit's place>ten's place So , possible unit digit = 2.3.4.5 when 2 is in unit's digit 1 must be in ten's and (3,4,5) forms the other numbers. total possible number =3!=6 similarly when 3 is in unit's digit 1 or 2 can be in ten's digit and 3 other digits form the number. so total possible number =3!*2=12 again when 4 ................. total possible number =3!*3=18 and when 5 .................. total possible number =3!*4=24 sum of total possibilities =6+12+18+24=60 Answer: B Manager Joined: 10 May 2018 Posts: 64 Re: How many numbers can be formed from 1, 2, 3, 4, 5 (without repetition) [#permalink] 19 Jan 2020, 03:42Does it mean a five digit number? A number can be 2 digit , 3 digit till 5 digit for this combination Posted from my mobile device Math Expert Joined: 02 Sep 2009 Posts: 86794 Re: How many numbers can be formed from 1, 2, 3, 4, 5 (without repetition) [#permalink] 19 Jan 2020, 03:46ManjariMishra wrote: Does it mean a five digit number? A number can be 2 digit , 3 digit till 5 digit for this combination Posted from my mobile device You are right. The question should mention that we are looking for 5-digit numbers only. Director Joined: 08 Aug 2017 Posts: 736 Re: How many numbers can be formed from 1, 2, 3, 4, 5 (without repetition) [#permalink] 19 Jan 2020, 04:05 Condi-1:Digit at unit place> digit at tens place. possible combinations for tens place and unit place, 5C2= 10. Here we will not multiply by 2! because we want ascending order. For example, (2,1) and (1, 2) are two pair but we need only (2,1) which is satisfying condition-1 For remaining places, arrangement of remaining digits is 3*2*1= 6.
GMAT Expert Joined: 16 Oct 2010 Posts: 13164 Location: Pune, India Re: How many numbers can be formed from 1, 2, 3, 4, 5 (without repetition) [#permalink] 02 Feb 2021, 22:12sharathnair14 wrote: How many five digit numbers can be formed from 1, 2, 3, 4, 5 (without repetition), when the digit at the unit’s place must be greater than that in the ten’s place? (a) \(54\) No of 5 digit numbers with 1, 2, 3, 4, 5 digits = 5! = 120 By symmetry, in half of them, the units digit will be greater that tens digit and in the other half, the tens digit will be greater than units digit. So 120/2 = 60 Answer (B) Note the symmetry - If 1 is in units digit, all such numbers will not be included. If 5 is in the units digit, all such numbers will be
included. If 2 is in units digit, only numbers with 1 is tens digit will be included. If 4 is in units digit, only number with 5 in tens digit will not be included. When 3 is in units digit, half the numbers will be acceptable and half will not be. Karishma For Individual GMAT Study Modules, check Study Modules > Re: How many numbers can be formed from 1, 2, 3, 4, 5 (without repetition) [#permalink] 02 Feb 2021, 22:12 Moderators: Senior Moderator - Masters Forum 3084 posts How many numbers of 5 digits can be formed using the digits 1 2 3 4 5 6 such that digits are repeated?The answer is 120 five-digit integers (5!= How many 5 digit numbers can be formed using the digits 1 2 3 4 and 5 Repetition not allowed?dat can b formed using 1,2,3,4,5 when repetitions is not allowed? Now the total no of possible ways in which these 5 no can be written without repetition are 5!= 120. How many 5 digit numbers can be formed from the digits 1 2 3 4 5 and 6 such that the numbers are divisible by 4 and their digits do not repeat?Therefore, there are a total of 192 numbers which can be formed using the digits 1,2,3,4,5,6 without repetition such that the number is divisible by 4. How many 5 digit numbers can be made from the digits 1 2 3 4 so that all the digits are taken in each number?For each such 4-digit number we can form we have 5 choices for the first digit (which cannot be 0), and with repetition allowed we have 6 choices for each of the last 3 digits. Therefore, we can form 5*6*6*6 = 1080 such 4-digit numbers. How many 5 digit numbers can be formed using digits 1,2 3 4 and 5 if repetition of digits is not allowed?hence the possibilities are 4×9×9×9=2916 numbers are possible. You listed 7 digits, each number with 5 positions, and that repetitions are allowed. So, this is simply 7⁵, which is 16,807. How many 5 digit numbers can be formed from the digits 1,2 3 4 5 and 6 such that the numbers are divisible by 4 and their digits do not repeat?Therefore, there are a total of 192 numbers which can be formed using the digits 1,2,3,4,5,6 without repetition such that the number is divisible by 4. How many 5 digit numbers can be formed using the digits 0 1,2 3 4 and 5 which are divisible by 5 without repetition of the digits?Answer : `=2xx5xx6xx6xx6=2160` ways. Step by step solution by experts to help you in doubt clearance & scoring excellent marks in exams. How many numbers of 5 digits can be formed with the digits 0 1,2 3 4 if the digits can repeat themselves?Since, repetition is not allowed, for the next significant place, 4 digits are available (since 0 can now be used). Sum of the digits = 0 + 1 + 2 + 3 + 4 = 10 which is not divisible by 3. ∴ None of the 5-digit numbers formed using the digits 0, 1, 2, 3, and 4 will not be divisible by 3. How many 5 digit numbers can be formed if repetition is allowed?<br> Repetition of digits is allowed. <br> `:. ` Each place out of unit, 10th, 100th and 1000th can be filled in 5 ways. <br> Now form multiplication rule <br> Total numbers `= 4 xx 5 xx 5 xx 5 xx 5 = 2500`.
How many 4 digit numbers can be made by using digits 1 to 7 repetition is not allowed if the digit 4 will always be there in the number?This is Expert Verified Answer
Total = 120*4= 480.
How many 7 digit numbers are there if repetition is not allowed?There are 9 digits you can have for the first digit (can't have 0). There are then 9 more for the second (all except the first one). Similarly there are 8 for the third, 7 for the 4th, etc… So the total would be 9*9*8*7*6*5*4 = 544,320 7 digit numbers without repeated digits.
How many 5 digit codes are possible if digits Cannot be repeated?1 Expert Answer
540 * 56 = 30240 zip codes without any repetitions.
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