Latest TCS Aptitude Question SOLUTION: In how many ways can 21 books on English and 19 books on Hindi be placed in a row on a shelf so that two books on Hindi may not be together?

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In how many ways can 21 books on English
and 19 books on Hindi be placed in a row on a
shelf so that two books on Hindi may not be
together?

Asked In TCS shikha (9 years ago)

Solved raj mohan Read Solution (15)

Is this Puzzle helpful?   (47)   (18) Submit Your Solution Permutation and Combination

Read Solution (15) :

jeet  (9 years ago)

X E X E X E X .... X E X
X represents Hindi books
E represents English books.
We,have 22 positions for hindi books nd 21 positions for placing english books.
Ways for placing 19 books in 22 positions =22p19
Placing 21 eng books = 21!
Total ways=
21!* 22p19.

Is this solution Helpfull? Yes (31) | No (6)  

raj mohan  (9 years ago) Best Solution

In order that two books on Hindi are never together, we must place all these books as under:

X E X E X E X .... X E X

where E - denotes the position of an English book and X that of a Hindi book.

Since there are 21 books on English, the number of places marked X are therefore, 22. Now, 19 places out of 22 can be chosen in

22C19 = 22C3 = 22 x 21 x 20 = 1540 ways.
3 x 2 x 1

Hence, the required number of ways = 1540.

Is this solution Helpfull? Yes (28) | No (15)  

Pratip Bhattacharyya  (9 years ago)

The solution talks about keeping 21 english books in a SPECIFIC order, when we get 22 slots between them so that we can place Hindi Books in them.
So the solution of 22C19 only gives us ways 19 hindi books can be placed in 22 slots. This is an arrangement with All english books in one order. We can still change the order of english books to get entirely new sets of arrangements. :)


No of ways 22 eng books can be arranged * No of ways 19 books can be arranged in 22 slots
= 21! * 22C19

Is this solution Helpfull? Yes (13) | No (5)  

subhi singh  (9 years ago)

first english books are placed in 21 ways. after that hindi books can be placed in 22c19 ways.hence answer will be 21*22c19

Is this solution Helpfull? Yes (3) | No (5)  

Raksha Shah  (9 years ago)

when 21 books on english r put in a row, there will b 22 spaces created, thus 19 books on hindi will have 22 spaces to fill in. this will give an ans of: 22C19
Ans= 22C19=1540 ways

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

raj mohan  (9 years ago)

In order that two books on Hindi are never together, we must place all these books as under:

X E X E X E X .... X E X

where E - denotes the position of an English book and X that of a Hindi book.

Since there are 21 books on English, the number of places marked X are therefore, 22. Now, 19 places out of 22 can be chosen in

22C19 = 22C3 = 22 x 21 x 20 = 1540 ways.
3 x 2 x 1

Hence, the required number of ways = 1540.

Is this solution Helpfull? Yes (2) | No (4)  

anitha thummalapally  (9 years ago)

In order that two books on Hindi are never together, we must place all these books as under:

X E X E X E X .... X E X

where E - denotes the position of an English book and X that of a Hindi book.

Since there are 21 books on English, the number of places marked X are therefore, 22. Now, 19 places out of 22 can be chosen in

22C19 = 22C3 = (22 x 21 x 20)/(3 x 2 x 1) = 1540 ways.

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

radha  (9 years ago)

english books arranged in 21ways
in 22 gaps 19 hindi books are arranged in22p19 ways
ans:21*22p19

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

Abhishek  (9 years ago)

Since, two Hindi books can not be together but 2 English book can.
So, 21 English books are arranged in 21! ways.
Now, there are 22 blank places like _E_E_E.......E_ where Hindi books can be placed.So,
Total no of arrangement= 21! * 22P19 ways

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

akshay kumar  (8 years ago)

21!*22p19*19!

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

akshata  (9 years ago)

22C19 ways

Is this solution Helpfull? Yes | No (2)  

SREEKANTH THUPILI  (9 years ago)

1540---->22C19

Is this solution Helpfull? Yes | No (4)  

aman vikram singh  (9 years ago)

EHEH......EE
ONE WAY IN WHICH LAST THREE PLACES CAN BE INTERCHANGED SO THIS MAKES 3
HEHE.....EE
SECOND WAY IN WHICH LAST FOUR PLACES CAN BE INTERCHANGES SO THIS MAKES 4
TOTAL 3+4=7

Is this solution Helpfull? Yes | No (6)  

kavana j  (8 years ago)

Let English book denoted by=E
Let Hindi book denoted by=H
it will be order like H E H E H E H.......H E H ,21 book on English so that number of mark H will be 22
19 out oh 22 i.e 22C19=22C3=(22*21*20)/(3*2*1)=1540
ans is 1540

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Sayantan Saha  (6 years ago)

22c19 is the answer

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