Latest TCS Aptitude Question SOLUTION: In how many ways can the letters of the English alphabet be arranged so that there are seven letters between the letters A and B, and no letter is repeated.

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(#M40024242) TCS Logical Reasoning question Keep an EYE

In how many ways can the letters of the English alphabet be arranged so that there are seven letters between the letters A and B, and no letter is repeated.

Asked In TCS Akhilesh Agrawal (10 years ago)

Unsolved Read Solution (30)

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Read Solution (30) :

Arpit Srivastava  (10 years ago)

24c7*7!*2!

Is this solution Helpfull? Yes (59) | No (27)  

Gopal Amreliya  (9 years ago)

A_ _ _ _ _ _ _ B and remaining 17
So moving this A and B 1 step to the right . still we have 7 letters in between.
So A and B can be shifted in the same manner to 18 more places.
Now SAME CAN BE APPLICABLE TO B_ _ _ _ _ _ _A SO 18 HERE.
NOW REMAINING ALPHABET ARE 24.
-> 18*2*24!
I.E. --> 36*24!

Is this solution Helpfull? Yes (59) | No (23)  

CHANDAN KUMAR  (9 years ago)

no. of ways of choosing 7 letters out of 24=24c7
no of ways of placing 7 letters w/o repitition=7!
no of ways of arranging 2 letters A and B= 2!
total no of ways=(24c7)*7!*2!

Is this solution Helpfull? Yes (27) | No (10)  

sandeep  (8 years ago)

We can fix A and B in two ways with 7 letters in between them. Now 7 letters can be selected and arranged in between A and B in 24P7 ways. Now Consider these 9 letters as a string. So now we have 26 - 9 + 1 = 18 letters
These 18 letters are arranged in 18! ways. So Answer is 2 x 24P7 x 18!
Infact, 2 x 24P7 x 18! = 36 x 24!.

Is this solution Helpfull? Yes (20) | No (2)  

Ravi Bhalani  (9 years ago)

There are P(24,7) arrangements of the letters of the alphabet (excluding A and B)taken ten at a time, and hence 2*P(24,7) strings of 9 letters, each beginning and ending with an a and
b(either letter coming first in a string).
For each of these strings, there are 18 ! ways to arrange the 17 remaining letters and the string.
So there are altogether 2*P(24,7)*18 ! arrangements of the desired type.

Is this solution Helpfull? Yes (16) | No (5)  

Animesh  (10 years ago)

ans will be 24!*2*18

Is this solution Helpfull? Yes (10) | No (11)  

areeba fatima  (9 years ago)

24p7*2!*18!
2! because AB are interchangeable
24p7 to select 7 alphabets out of 24 alphabets
18! because we hace considered the 9 letters set as one letter and arranged rest of the letters
hence 24p7*2!*18!

Is this solution Helpfull? Yes (9) | No (5)  

rt  (9 years ago)

24p7*2!
out of 24 we have to opt 7 letters(26-A&B)
and 2! for A&B

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

aman jaiswal  (10 years ago)

24c7 *7!*2!

Is this solution Helpfull? Yes (5) | No (2)  

harinee  (8 years ago)

Answer: 36 * 24! or 24P7 * 2 * 18!
Explanation:
We can fix A and B in two ways with 7 letters in between them. Now 7 letters can be selected and arranged in between A and B in 24P7 ways. Now Consider these 9 letters as a string. So now we have 26 - 9 + 1 = 18 letters
These 18 letters are arranged in 18! ways. So Answer is 2 x 24P7 x 18!
Infact, 2 x 24P7 x 18! = 36 x 24!. So go for Option B as it was given as OA.

Is this solution Helpfull? Yes (5) | No   

torsha mandal  (7 years ago)

Excluding A and B, there is a total of 24 letters in the alphabet. Out of that, 7 letters are to be selected and arranged between them. Thus to select and arrange 7 letters from 24 letters ==> 24P7 and so now we have arranged 9 letters including A and B.
The remaining 17 letters can be arranged in 17! ways.
But it is not necessary that A is in the 1st position followed by 7 letters and B is in the 9th position.B can be anywhere from the 9th position to the last 26th position like
A_ _ _ _ _ _ _ B _ _ _ _ _ _ upto 26th.... , _A _ _ _ _ _ _ _ B _ _ _ _ upto 26th...., and so on. Thus there are 18 ways to fill the letters A and B.

And finally it is also not necessary that A must be before those 7 letters and B after them. It can also be as B followed by those 7 letters followed by A.(B_ _ _ _ _ _ _A_ _....) . Thus there are two ways of arranging them.

To conclude the total number of ways is,
24P7 * 17! * 18 * 2!
==> 24! / (24-7)! * 17! * 36
Total ways = 24! * 36

Is this solution Helpfull? Yes (3) | No   

siddharth  (10 years ago)

total ways=22*21*20*19*18*17*16*15*14*2
2 ways for changing the position of A and B

Is this solution Helpfull? Yes (2) | No (9)  

darshan soni  (10 years ago)

ans is 2*sqrt(2)/3

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

surekha divvela  (8 years ago)

24p7*2*18!

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

Shubham Choudhary  (8 years ago)

We can fix A and B in two ways with 7 letters in between them. Now 7 letters can be selected and arranged in between A and B in 24P7 ways. Now Consider these 9 letters as a string. So now we have 26 - 9 + 1 = 18 letters
These 18 letters are arranged in 18! ways. So Answer is 2 x 24P7 x 18!
Infact, 2 x 24P7 x 18! = 36 x 24!

Is this solution Helpfull? Yes (2) | No   

siddharth  (10 years ago)

A_ _ _ _ _ _ _ B

first place= 22
second plac=21
third=20
.
.
.
seventh=14
total ways= 22*21*20*19*18*17*16*15*14

Is this solution Helpfull? Yes (1) | No (13)  

shrey  (9 years ago)

2*18*24!

2 because a,b and b,a
24! because except a and b other can select any place
18 because group a-b can place in 24 by 18 ways

Is this solution Helpfull? Yes (1) | No (3)  

raja priyan  (9 years ago)

24c7*7!*2!

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

arju  (8 years ago)

2 x 24P7 x 18!

Is this solution Helpfull? Yes (1) | No   

Arun Kante  (8 years ago)

24p7*2 ... is correct answer

Is this solution Helpfull? Yes (1) | No   

Latha  (8 years ago)

24c7*7!*2*18!

Is this solution Helpfull? Yes (1) | No   

ranjan kumar  (9 years ago)

can anyone give its proceedings..??

Is this solution Helpfull? Yes | No (1)  

abhisek banerjee  (9 years ago)

only gopal amreliya is correct .all other answers are wrong including first one

Is this solution Helpfull? Yes | No (1)  

BASANT KUMAR  (9 years ago)

24*23*22*21*20*19*18

Is this solution Helpfull? Yes | No   

rakesh kumar  (9 years ago)

sorry forgot to mention about the a&b they also can interchange so..24c7*7!*18!*2!=36*24!

Is this solution Helpfull? Yes | No   

Ramanuj Pande  (8 years ago)

26 P 7=26!/19!
there are 26 letters in English alphabet
only 7 letters should be between A and B
so it can be solved by using permutation.

Is this solution Helpfull? Yes | No   

Nemai Layek  (8 years ago)

This is not a question in "Blood Relation" topic !!!!!

Is this solution Helpfull? Yes | No   

prateek goswami  (8 years ago)

A can be at 1st position and B can be at 9th position,A can be at 2nd position then B can be at 10th position and so on...
this can be arrange in 18 ways
a and b can be arrange in 2 ways
and rest 24 alphabet can be arrange in 24!
so answer can be given as 2*18*24!

Is this solution Helpfull? Yes | No   

ABDUL KARIM  (7 years ago)

We can fix A and B in two ways with 7 letters in between them. Now 7 letters can be selected and arranged in between A and B in 24P724P7 ways. Now Consider these 9 letters as a string. So now we have 26 - 9 + 1 = 18 letters
These 18 letters are arranged in 18! ways. So Answer is 2 x 24P724P7 x 18!
Infact, 2 x 24P724P7 x 18! = 36 x 24!. So go for Option B as it was given as OA.

Is this solution Helpfull? Yes | No   

PC  (6 years ago)

Now the remaining number of letters are 24. Next we have to select 5 from 24 i.e no of ways of selection and arranging is 24C5*5! .A and B can be arranged at either sides so two ways of arranging A and B.
Therefore total no of ways=24C5*5!*2

Is this solution Helpfull? Yes | No   

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