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Yale Moderator G
Joined: 05 May 2019
Posts: 180
GPA: 3
How many numbers can be formed from 1, 2, 3, 4, 5 (without repetition)  [#permalink]

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4 00:00

Difficulty:   75% (hard)

Question Stats: 38% (01:52) correct 63% (02:31) wrong based on 32 sessions

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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.
GMAT Tutor G
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Re: How many numbers can be formed from 1, 2, 3, 4, 5 (without repetition)  [#permalink]

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Top Contributor
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
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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Manager  G
Joined: 13 Aug 2018
Posts: 59
Re: How many numbers can be formed from 1, 2, 3, 4, 5 (without repetition)  [#permalink]

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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

Manager  B
Joined: 10 May 2018
Posts: 75
Re: How many numbers can be formed from 1, 2, 3, 4, 5 (without repetition)  [#permalink]

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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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Math Expert V
Joined: 02 Sep 2009
Posts: 61302
Re: How many numbers can be formed from 1, 2, 3, 4, 5 (without repetition)  [#permalink]

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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

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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Director  P
Joined: 08 Aug 2017
Posts: 692
Re: How many numbers can be formed from 1, 2, 3, 4, 5 (without repetition)  [#permalink]

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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. 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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