Latest TCS Aptitude Question SOLUTION: How many 6 digit even numbers can be formed from digits 1 2 3 4 5 6 7 so that the digit should not repeat and the second last digit is even? a)6480 b)320 c)2160 d)720

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How many 6 digit even numbers can be formed from digits 1 2 3 4 5 6 7 so that the digit should not repeat and the second last digit is even?
a)6480 b)320 c)2160 d)720

Asked In TCS kirankarthik (11 years ago)

Unsolved Read Solution (32)

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Read Solution (32) :

srikanthpatnamshetty  (11 years ago)

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given 6th digit even number , so last digit 2 or 4 or 6-> 3 ways
" 5th digit should be even...so there will be 2 ways(rep. not allowed)
so,therefore we get 5*4*3*2*2*3=720 ways

Is this solution Helpfull? Yes (61) | No (17)  

Gaurang Dhake  (11 years ago)

there are six digits..
a b c d e f(say)
f=possible digits are 3 -(2,4,6)
e=possible 2 digits - (2,4,6)
and then rest...
d=possible 5 digits
c=possible 4 digits
b=possible 3 digits
a=possible 2 digits

the digits goes on decreasing since digits are not supposed 2 b repeated...
hence ans=>3*2*5*4*3*2=720...:)

Is this solution Helpfull? Yes (33) | No (4)  

ravi palla  (9 years ago)

_ _ _ _ _ _
last 2 digits should be even numbers.
so 3p2 ways.
remaining 4 digits should be filled with 5 numbers,becz no numbr is repeated.
so 5P4 ways.

ans=3P2*5P4=720

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

DEEPAK KUMAR  (8 years ago)

6th digit is filled by any one from 2,4,6
5th digit is placed by any 6 no,
4th digit is placed by any 5 no,
3rd digit is placed by any 4 no,
2nd digit is placed by any 3 no,
1st digit is placed by any 2 no,
2*3*4*5*6*3=2160

Is this solution Helpfull? Yes (10) | No (10)  

PURBASHA ROY  (8 years ago)

second last digit is even.
so, _ _ _ _ 2 _
_ _ _ _ 4 _
_ _ _ _ 6 _

3 cases are possible.
Now,1st vacant position can be filled up in 6 ways as 1 digit is fixed and we have to select it from rest 6 digits.
Similarly 2nd position can be filled up in 5 ways
3rd position can be filled up in 4 ways
4th position can be filled up in 3 ways
6th position can be filled up in 2 ways
So, total no of ways per case=6*5*4*3*2=720 ways.
So, for 3 cases total no of ways= 3*720=2160

Is this solution Helpfull? Yes (7) | No   

Taruna  (11 years ago)

let no. be a b c d e f
then possible case for e=3
for f=2
possible case for a =5(total dig=7,1 used)
for b=4
for c=3
for d=2
so 5*4*3*2*3*2=720

Is this solution Helpfull? Yes (6) | No (3)  

JIT BHATTACHARJEE  (8 years ago)

ans is=3*6P5=2160

Is this solution Helpfull? Yes (6) | No (7)  

sunil yadav  (9 years ago)

there are six digits..
a b c d e f(say)
f=possible digits are 3 -(2,4,6)
e=possible 2 digits - (2,4,6)
and then rest...
d=possible 5 digits
c=possible 4 digits
b=possible 3 digits
a=possible 2 digits

the digits goes on decreasing since digits are not supposed 2 b repeated...
hence ans=>3*2*5*4*3*2=720...:)

Is this solution Helpfull? Yes (3) | No   

nivetha sekar  (8 years ago)

Since it has been given to form 6 digit even number the last digit has to be one of the digits in either 2or 4 or 6 so its probability is
3P1
The condition given for the second last digit is" it should be the even number" since we have already placed one of the even number to the last digit from the remaining 2 digits we should fill the second last digit so
2P1
for the remaining places we are going to fill it with 4 digits among 5 because of the reason no repetition is allowed so
5P4
SOLUTION:
3*2*5*4*3*2 = 720
Since all the condition has to be satisfied to get the 6 digit number.

Is this solution Helpfull? Yes (3) | No   

Alwin Davis  (9 years ago)

We have to form six digit numbers; so I will represent it as _ _ _ _ _ _
>Here the last two digits should be even
>Out of the available 7 digits , 3 are even
So the first 4 positions have 5*4*3*2 = 120 possibilities
Now the last 2 positions can be filled in 3*2 = 6 ways
Therefore the 6 digit no can be formed in 120*6=720 ways

Is this solution Helpfull? Yes (1) | No   

Kanika Rana  (8 years ago)

d is the ans
5! x 3! =720

Is this solution Helpfull? Yes (1) | No   

Deepak Kolte  (8 years ago)

Total kilometers travelled by 4 tyre = 40000 × 4 = 1,60,000. This has to be share by 5 tyres. So each tyre capacity = 1,60,000 / 5 = 32, 000. You have a doubt, after we travel 32,000 km, we are left with 4 worn tyes and one new tyre. But If the tyres are rotated properly after each 8000 km, all the tyres are equally used.

Is this solution Helpfull? Yes (1) | No   

sivagamy  (8 years ago)

Here they are talking about last two digit , that too should be in even . so consider even number from given question 2,4,6
possible ways are - - - - 24,- - - - 42,- - - - 46,- - - - 64,- - - -26,- - - - 62.
So 6! ways=720 is answer

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

swagat kumar dishri  (8 years ago)

720
5*4*3*2*2*3

Is this solution Helpfull? Yes (1) | No   

Jitheesha J  (5 years ago)

720
2x3x4x5x3x2 ways

Is this solution Helpfull? Yes (1) | No   

Subhramalya  (9 years ago)

3 * 6p5 =3*720=2160

Is this solution Helpfull? Yes | No (1)  

bakya  (8 years ago)

5*4*3*2*2*3=720
so answer is d)720

Is this solution Helpfull? Yes | No (1)  

shivank garg  (8 years ago)

5*4*3*2*2*3=720

Is this solution Helpfull? Yes | No (2)  

syed ali  (8 years ago)

we have to form 6 digits even number ,
_ _ _ _ _ _

so the last digit must be even. then only it is divisible by any even number
here the condition is the last before digit must be also even
there are three even numbers so the possibility of filling last digit is 3
and the possibility of filling before last digit is 2
remaining number including four odd number and 1 even number , therefore totally 5
the combination is
5*4*3*2*2*3=720

Is this solution Helpfull? Yes | No   

Soham Dey  (8 years ago)

5!*2*3=720...

Is this solution Helpfull? Yes | No (2)  

vyjayanthi  (8 years ago)

ans.D)

if we have to form even nmbers, unit's digit must be 2,4,6 i.e., 3 ways. Also 5th digit must be even so it can be filled in 2 ways . Now remaining 5 digits can be filled in 5! ways.
so total 5!*3*2=720 ways.

Is this solution Helpfull? Yes | No   

Devdatta mane  (7 years ago)

Ans is 720.

Is this solution Helpfull? Yes | No   

chanoja  (7 years ago)

answer is 720

Is this solution Helpfull? Yes | No (1)  

Ashtalakshmi  (7 years ago)

there are 6 digits.
- - - - - -
last digit should be even.(2,4,6) _ _ _ _ _ _3 ways.
second last is even..there are 3 even numbers.we have to use one even number for last digit and remaining two even numbers for second last digit.
_ _ _ _ _2 ways _3ways..
5* 4*3*2*3=720 was.

Is this solution Helpfull? Yes | No   

minu raj  (5 years ago)

There are 7 digits and we have to form 6digit even nos.
For a no to even , the last digit should be either(2,4,6)
a/q the 2nd last digit should also be even (2,4,6)
A/q no digits should repeat.
therefore, last digit 3p1
second last digit 2p1
___ ___ ___ ___ ___ ____(last both places are filled)
first place can be filled by 5 digits remaining ,5p1
2nd=4p1
3rd =3p1
4th=2p1
on solving,
5*4*3*2*2*3=720

Is this solution Helpfull? Yes | No   

sarumathipriya  (5 years ago)

6 digit even number so that the last digit will be 2 or 4 or 6 hence remaining 1357(246)
totally 5! and the 2, 4, 6 has 3! so 5!*3!=1*2*3*4*5*1*2*3=720

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seera sowmya  (5 years ago)

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5*4*3*2*2*3=720

Is this solution Helpfull? Yes | No   

Mohd Arfat Abbas Shaikh  (5 years ago)

To form 6-digit even number, the last digit should be an even number so 3 ways (2, 4, or 6) to fill the last digit and second last digit also should be even for which it will take 2 ways to fill.
The last two digits are filled in 6 ways( 2 x 3 = 6 ways). The rest of the 4 digits can be filled in 5P4 ways i.e. 120 ways. Hence altogether to fill 6-digit even number = 120 * 6 = 720 ways.

Is this solution Helpfull? Yes | No   

charan  (5 years ago)

given 6 digit even taken as given number last digits filled with 2,4,6 in 3 ways
next condition 5 th digit filled with 2 ways without repitition.
so we get answer like 5*4*3*2*2*3 = 720

Is this solution Helpfull? Yes | No   

umesh kumar  (4 years ago)

6P5*1*3=2160

Is this solution Helpfull? Yes | No   

gowtham  (4 years ago)

there are six digits..
a b c d e f(say)
f=possible digits are 3 -(2,4,6)
e=possible 2 digits - (2,4,6)
and then rest...
d=possible 5 digits
c=possible 4 digits
b=possible 3 digits
a=possible 2 digits

the digits goes on decreasing since digits are not supposed 2 b repeated...
hence ans=>3*2*5*4*3*2=720.gowti

Is this solution Helpfull? Yes | No   

Priyank  (1 year ago)

720
5! x 4! x 3! x 2! x2! x3

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