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How many numbers can be formed from 1, 2, 3, 4, 5 (without repetition)

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How many numbers can be formed from 1, 2, 3, 4, 5 (without repetition)  [#permalink]

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New post 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) \(120\)

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)  [#permalink]

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New post 11 Jan 2020, 08:59
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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)  [#permalink]

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New post 19 Jan 2020, 01:24
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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)  [#permalink]

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New post 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)  [#permalink]

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New post 19 Jan 2020, 03:46
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Re: How many numbers can be formed from 1, 2, 3, 4, 5 (without repetition)  [#permalink]

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New post 19 Jan 2020, 04:05
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] 19 Jan 2020, 04:05
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