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

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sharathnair14
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How many numbers can be formed from 1, 2, 3, 4, 5 (without repetition) [#permalink] New post   Updated on: 20 Jan 2020, 06:37
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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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B

Originally posted by sharathnair14 on 10 Jan 2020, 10:38.
Last edited by sharathnair14 on 20 Jan 2020, 06:37, edited 1 time in total.
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How many numbers can be formed from 1, 2, 3, 4, 5 (without repetition) [#permalink] New post   Updated on: 15 Jul 2020, 10:45
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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!

Originally posted by BrushMyQuant on 11 Jan 2020, 09:59.
Last edited by BrushMyQuant on 15 Jul 2020, 10:45, 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] New post   19 Jan 2020, 02:24
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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] New post   19 Jan 2020, 04:42
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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] New post   19 Jan 2020, 04:46
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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] New post   19 Jan 2020, 05:05
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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] New post   02 Feb 2021, 23:12
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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) \(54\)
(b) \(60\)
(c) \(17\)
(d) \(2 × 4!\)
(e) \(120\)


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.
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Re: How many numbers can be formed from 1, 2, 3, 4, 5 (without repetition) [#permalink] New post   23 Aug 2023, 21:33
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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?

We will consider pairs for the digit at the unit’s place and that in the ten’s place,
(2,1)(3,1)(4,1)(5,1)(3,2)(4,2)(5,2)(4,3)(5,3)(5,4) = 10

The other 3 places can be arranged in 3! ways i.e. 6 ways

Therefore required ways = 6x10=60 ways

Hence B
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Re: How many numbers can be formed from 1, 2, 3, 4, 5 (without repetition) [#permalink]
23 Aug 2023, 21:33
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