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How many numbers can be formed from 1, 2, 3, 4, 5 (without repetition)
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Updated on: 20 Jan 2020, 05:37
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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) \(120\)
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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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Re: How many numbers can be formed from 1, 2, 3, 4, 5 (without repetition)
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11 Jan 2020, 08:59
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=6 Numbers with Unit's digit greater than the ten's digit 123, 213, 312 Numbers with Ten's digit greater than the unit's digit 321, 132, 231 So total Number of cases = 120/2 = 60 So, Answer will be B Hope it helps! 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) \(120\)
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Re: How many numbers can be formed from 1, 2, 3, 4, 5 (without repetition)
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19 Jan 2020, 01:24
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 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



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Re: How many numbers can be formed from 1, 2, 3, 4, 5 (without repetition)
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19 Jan 2020, 03:42
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)
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19 Jan 2020, 03:46
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 5digit numbers only.
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Re: How many numbers can be formed from 1, 2, 3, 4, 5 (without repetition)
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19 Jan 2020, 04:05
Condi1:Digit at unit place> digit at tens place. Condi2: 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 condition1
For remaining places, arrangement of remaining digits is 3*2*1= 6. So total ways of arrangement= 6*10= 60. B is answer.




Re: How many numbers can be formed from 1, 2, 3, 4, 5 (without repetition)
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19 Jan 2020, 04:05






