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How many numbers can be formed from 1, 2, 3, 4, 5 (without repetition) [#permalink]
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Question Stats: 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) \(54\)(b) \(60\)(c) \(17\)(d) \(2 × 4!\) (e) \(120\)
Originally posted by sharathnair14 on 10 Jan 2020, 09:38.
GMAT Tutor Joined: 05 Apr 2011 Status:Tutor - BrushMyQuant Posts: 1385 Location: India Concentration: Finance, Marketing Schools: XLRI (A) 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.Now, in half them unit's digit will be bigger than the ten's digit and in half of them it will be smaller.Example: Let's say we have three digits 1,2,3. Total number of numbers without repeating digits = 3*2*1=6Numbers with Unit's digit greater than the ten's digit123, 213, 312Numbers with Ten's digit greater than the unit's digit321, 132, 231So total Number of cases = 120/2 = 60So, Answer will be BHope it helps! _________________
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) \(54\)(b) \(60\)(c) \(17\)(d) \(2 × 4!\) (e) \(120\) unit's place>ten's placeSo , possible unit digit = 2.3.4.5when 2 is in unit's digit 1 must be in ten's and (3,4,5) forms the other numbers.total possible number =3!=6similarly 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=12again when 4 ................. total possible number =3!*3=18and when 5 .................. total possible number =3!*4=24sum of total possibilities =6+12+18+24=60Answer: 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: 86975
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. _________________
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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.Condi-2: Without repetition(1,2,3,4,5) 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. So total ways of arrangement= 6*10= 60. B is answer.
GMAT Expert Joined: 16 Oct 2010 Posts: 13222 Location: Pune, India
Re: How many numbers can be formed from 1, 2, 3, 4, 5 (without repetition) [#permalink]
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) \(54\)(b) \(60\)(c) \(17\)(d) \(2 × 4!\) (e) \(120\) No of 5 digit numbers with 1, 2, 3, 4, 5 digits = 5! = 120By 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 = 60Answer (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. _________________
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Re: How many numbers can be formed from 1, 2, 3, 4, 5 (without repetition) [#permalink] 02 Feb 2021, 22:12 |
How many numbers can be formed from 1,2 3.4 5 without repetition when the digit at the units place must be greater than that in the tens place?
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