Latest TCS Aptitude Question SOLUTION: find the no of 6-digit numbers that can be formed using the digits 1,2,3,4,5,6 once such that the 6-digit nos divisible by its unit digit?

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find the no of 6-digit numbers that can be formed using the digits 1,2,3,4,5,6 once such that the 6-digit nos divisible by its unit digit?

Asked In TCS Gourab Dutta (9 years ago)

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Fakir Mohan Nayak  (9 years ago)

ans 648

If the unit place is 1,2,3,5,6 there are 120 ways to construct 6 digit numbers for each.If the unit digit is 4 then the number of ways is(4*3*2*1*2*1)=48 ways..

So total number of 6 digits formed is(5*120+48)=648

Is this solution Helpfull? Yes (22) | No (1)  

nmtsaikumar  (9 years ago)

There are 6 numbers which can be placed in units digits.
case 1: When the unit digit is 1,2,3,5,6 whatever the other numbers are the 6 digit number will be surely divisible by the unit digit.
Hence the 5 numbers in the units place can be placed in 5 ways and the remaining 5 numbers can be arranged in 5! ways.
5*5!=600 ways
Case 2: If the unit digit is 4, then the tens digit should be 2 or 6, hence 24 or 64 can be arranged in the last two places in 2 ways and the remaining 4 numbers can be arranged in 4 places in 4!ways.
2*4!=48 ways


Total no.of.ways= 600+48 = 648 ways.

Is this solution Helpfull? Yes (5) | No   

c.bhumika  (9 years ago)

plzz giv correct answer ...

Is this solution Helpfull? Yes (3) | No   

atrijit  (9 years ago)

ans 72.
the units place cant be 1 since all the numbers are divisible by 1
the units place cant be 2 since all even numbers will be divisible by 2
the units place cant be 3 since sum of all the digits=21 which is divisible by 3 implying the number is also div by 3
Similarly the units digit cant be 5 and 6 as well
So it leaves out only 4
Now if units place is 4 the tenths place cant be 2 or 6 since 24 or 64 are divisible by 4.So the tenths place can be filled in 3 ways and the rest places in 4! ways.
Therefore ans is 24*3=72.

Is this solution Helpfull? Yes (2) | No (13)  

Abhinav Akash  (9 years ago)

There are six numbers which can be placed in unit digit.
case-1 When the unit digit is 1,2,3,5,6 whatever the other numbers are the 6 digit number will be surely divisible by the unit digit.
Hence the 5 numbers in the units place can be placed in 5 ways and the remaining 5 numbers can be arranged in 5! ways.
5*5!=600 ways
Case 2: If the unit digit is 4, then the tens digit should be 2 or 6, hence 24 or 64 can be arranged in the last two places in 2 ways and the remaining 4 numbers can be arranged in 4 places in 4!ways.
2*4!=48 ways


Total no.of.ways= 600+48 = 648 ways.

Is this solution Helpfull? Yes (2) | No   

indrajeet singh  (9 years ago)

ans 648

if the unit place digit is 1,2,3,5,6 there are 120 ways to costruct 6 digit no for each.if unit digit is 4 then [||||(2,6)|4] the no of ways is 4*3*2*1*2*1=48 ways...

Is this solution Helpfull? Yes (1) | No (2)  

akshay  (9 years ago)

1,2,3,5 will nt form any no..!!
bt in d case of 4..it form only those no in which ten digit contain 1,3,5 so no will be 1*2*3*4*3*1=72
6 will also doesnt form any no..bcz in any case it will divisible by 2*3

Is this solution Helpfull? Yes | No (9)  

satyam  (9 years ago)

if unit digit is 1 then 5!= 120
if unit digit is 2 then 5!= 120
if unit digit is 3 then 5!= 120(sum is 21)
if unit digit is 5 then 5!= 120
if unit digit is 6 then 5!= 120
if unit digit is 4 then 2*4!=48 (24,64 only)
total = 648
and we can arrange total in 6!=720 ways
720-648=72

Is this solution Helpfull? Yes | No (2)  

samiksha kapoor  (9 years ago)

Is it 72 or 648 which is correct??????

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VIVEK JAIN  (8 years ago)

648 is right answer

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