How many numbers can be formed from 1,2,3,4,5 without repeating, where the digit at the unit's place must be greater than that in the ten's place? CAT 1998
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Or, to do it directly, we have $8\cdot 9\cdot 8\cdot7\cdot6+7\cdot 8\cdot 7\cdot 6+6\cdot 7\cdot 6+5\cdot 6+4=24192+2352+252+30+4=26830$.
Here I have just added the number of five digit numbers without repitition greater than $12345$ of the form $abcde,\, a\gt1$, $1bcde,\,b\gt2$, $12cde,\,c\gt3$, $123de,\,d\gt4$ and, finally, $1234e,\,e\gt5$.
How many numbers can be formed from 1, 2, 3, 4, 5 (without repetition) [#permalink]
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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) \(120\)
Originally posted by sharathnair14 on 10 Jan 2020, 09:38.
Last edited by sharathnair14 on 20 Jan 2020, 05:37, edited 1 time in total.
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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.
Last edited by BrushMyQuant on 15 Jul 2020, 09:45, edited 1 time in total.
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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
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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
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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
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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.
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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