So basically, I attempted this question as- There are 4 numbers and 3 places to put in the numbers: In the ones place, any 4 numbers can be put, so there are 4 choices in the ones place. Similarly for the tens and the hundreds place. So, the total choices are, by multiplication principle- $$4*4*4=64$$ And well and good, this was the answer. But what if I reversed the method? So I take some particular numbers, like $1,2,3$ and say that, well, $1$ can go in $3$ places, $2$ in $2$ places and $3$ in $1$ place, so by multiplication principle, there are $6$ ways of forming a $3$-digit number with $1,2,3$. But there are $4$ different numbers. So the number of $3$-number combinations are- $(1,2,3)$,$(1,2,4)$,$(1,3,4)$,$(2,3,4)$. Each can be arranged in $6$ ways, so we get $24$ ways totally. So why is my answer different here?  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: 170 GPA: 3 How many numbers can be formed from 1, 2, 3, 4, 5 (without repetition)
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Hide 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: 1137 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]
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]
sharathnair14 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]
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 Math Expert Joined: 02 Sep 2009 Posts: 86776 Re: How many numbers can be formed from 1, 2, 3, 4, 5 (without repetition) [#permalink]
ManjariMishra 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: 735 Re: How many numbers can be
formed from 1, 2, 3, 4, 5 (without repetition) [#permalink]
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: 13161 Location: Pune, India
Re: How many numbers can be formed from 1, 2, 3, 4, 5 (without repetition)
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sharathnair14 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 two digit numbers can be generated using the digits 1,2 3 4 without repeating any digit?Hence, the total 2 digits number are 12.
How many 4 digits numbers that can be formed from the digits 1,2 3 4 5 so that digits do not repeat and it is an even number?Hence, there are 48 four digit even numbers that can be formed using the digits 1, 2, 3, 4, 5 if no digit is repeated.
How many 3Problem 2: How many 3-digit even numbers can be formed from the digits 1, 2, 3, 4, 5, 6 if the digits can be repeated? Solution: Answer: 108.
How many 4 digit numbers can you make without repeating digits?So there are 210 different combinations of four digits chosen from 0-9 where the digits don't repeat.
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