How many numbers can be formed from some or all of the digits 2.3.4.5 if number do not have
repeated digits?
Answers
Step-by-step explanation:
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GMAT Club Forum Index Problem Solving (PS)
How many numbers can be formed from 1, 2, 3, 4, 5 (without repetition) : Problem Solving (PS)
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sharathnair14
Updated on: Jan 20, 2020

00:00
A
B
C
D
E
DIFFICULTY:
   75% (hard)
QUESTION STATS:
based on 34 sessions
44% (01:51) correct
56% (02:25) wrong
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) 
(b) 
(c) 
(d) 
(e) 
Spoiler: OA
Last edited by sharathnair14 on 20 Jan 2020, 05:37, edited 1 time in total.
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BrushMyQuant
EXPERT'S
POST
Updated on: Jul 15, 2020
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!
Last edited by BrushMyQuant on 15 Jul 2020, 09:45, edited 1 time in total.
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jackfr2
Jan 19, 2020
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) 
(b) 
(c) 
(d) 
(e) 
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:
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
Step-by-step explanation: