Latest TCS Aptitude Question SOLUTION: hw many 6 dgts numbrs cn be made using digits 1,2,3,4,5,6 without repetiotin such that hundread's digit is greater than ten's digit and ten's is greater than ones digit?? Give any

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(#M40038053) TCS Numerical Ability question Keep an EYE

hw many 6 dgts numbrs cn be made using digits 1,2,3,4,5,6 without repetiotin such that hundread's digit is greater than ten's digit and ten's is greater than ones digit??
Give any short hand explanation if possible.

Asked In TCS shivaprasad (9 years ago)

Unsolved Read Solution (12)

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Read Solution (12) :

sai  (9 years ago)

let hunderds place with 3 then possible cases
3: 3 2 1
4: 4 3 2
4 3 1
4 2 1
5: 5 4 3
5 4 2
5 4 1
5 3 2
5 3 1
5 2 1
6: 6 5 4
6 5 3
6 5 2
6 5 1
6 4 3
6 4 2
6 4 1
6 3 2
6 3 1
6 2 1
so total combinations : 20*6=120

Is this solution Helpfull? Yes (41) | No (3)  

onica  (9 years ago)

6 numbers can be arranged in 6! ways and according to the condition Hundereds>tens>ones they cannot interchange there postions so they are identical an can be arranged in 3! ways so,
6!/3!=120

Is this solution Helpfull? Yes (16) | No (1)  

suman kumar  (9 years ago)

the correct answer is 180.
last 2 digit 21=24
last 2 digit 31=18
last 2 digit 41=12
last 3 digit 651=6
last 2 digit 32=18
last 2 digit 42=12
last 2 digit 652=6
last 2 digit 43=12
last 3 digit 653=6
last 3 digit 654=6
total-120

Is this solution Helpfull? Yes (3) | No (2)  

arjit  (9 years ago)

there are 6 numbers 1,2,3,4,5,6

leaving tens hundreds and units place the remaining three places could be filled in

6*5*4*(hundreds>tens>unit)

so the last three places could be filled in only 1 way if 3 digits are left

so the answer is 6*5*4=120

Is this solution Helpfull? Yes (3) | No   

Udai Pratap Singh  (9 years ago)

step1 :-you have 6 place last 3 digit have some condition
but starting 3 digit can be arrange by 3*2*1=6
step2 :-at hundred position only 4 option available=6,5,4,3
(we can not include 2 and 1 because of condition ,give in question)
step3 :-if we place 6 at hundred position then at ten's digit we can put only
one of the 4 number and at unit digit we have 4 option too
so total 1*4*4=16 posibility.

4 case and posible combinition...
100 10 unit
6(number) 4 4 =1*4*4=16
5 3 3 =1*3*3=9
4 2(3 or 2) 2(2 or 1)=1*2*2=4
3 1(only 2) 1(only 1)=1*1*1=1

total=30 combination for last 3 digit and we know 6 combination for stating
digit.
so

ans is =6*30=[180] ...:

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

shivam  (9 years ago)

what is the correct answer?

Is this solution Helpfull? Yes (2) | No   

AMIT KUMAR SINGH  (9 years ago)

CORRECT ANSWER IS 120

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

gaurav kumar  (9 years ago)

we have to select 6 number in which condition is to be satisfied first so last three digit can be slected in 6c3 ways and remaining 3 digit can be occupied in 3 places with 3! so simultaneously it can be placed in 3!*6c3 ie 120 is the ans

Is this solution Helpfull? Yes (2) | No   

avishek sen  (9 years ago)

sorry for my previous ans.....
In one's digit ----> 1,2,3,4 = 4 numbers can b placed
In ten's digit ----> 2,3,4,5 = 4 numbers can b placed
In hundreads's digit ----> 3,4,5,6 = 4 numbers can b placed

In rest 3 places 1,2,3,4,5,6 shpuld b placed in 6c3=20 ways
So, total 6 dgts number cn b made=4+4+4+20=32 ways...(ans.)

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

Satish Gampala  (9 years ago)

N articles (n1,n2,n3 .... nN) to be arranged in N places such that ni comes before nj, nj comes before nk then...

Total no of articles have restricted to their positions is = 3 -->>(ni,nj,nk)


then no off possibilities is ==>>> (n C 3)*(n-3)!

6 C 3* 3! === 120

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

s.suhasini  (9 years ago)

Ans is 22*6:132

Is this solution Helpfull? Yes | No (8)  

avishek sen  (9 years ago)

In one's digit ----> 1,2,3,4 = 4 numbers can b placed
In ten's digit ----> 2,3,4,5 = 4 numbers can b placed
In hundreads's digit ----> 3,4,5,6 = 4 numbers can b placed

In rest places 1,2,3 shouldn't b placed....
So 6,5,4 should b placed in rest places in 3!=6 ways

So, total 6 dgts number cn b made=4+4+4+6=18 ways...(ans.)

Is this solution Helpfull? Yes | No (4)  

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