Aptitude - Permutation and Combination - Discussion
Discussion Forum : Permutation and Combination - General Questions (Q.No. 14)
14.
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?
Answer: Option
Explanation:
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.
Discussion:
27 comments Page 1 of 3.
Nikhil Tambi said:
2 decades ago
How there are only 19 spaces left for books X, and why we are calculating 22C3 instead of 22C19?
Balakumar said:
2 decades ago
Hi Nikhil,
The value of 'r' in combination can be replaced by (n-r), we can use the value which ever is simpler to calculate.
Thank You.
The value of 'r' in combination can be replaced by (n-r), we can use the value which ever is simpler to calculate.
Thank You.
Yog said:
2 decades ago
What is the difference between permutation and combination?
Ananth said:
2 decades ago
Hi Nikhil,
nCr = nC (n-r).
nCr = nC (n-r).
Ananth said:
2 decades ago
Here why we are taking 19 english books instead of 21. Let E denotes english and H denotes hindi. Then the order of arrangement will be EHEHEHEH...HE. Here in this method we get 20 english with the starting and ending one.
Phanindra said:
2 decades ago
Why he begin arrangment with hindi book? and how he got the 22 places?
Pallavi said:
2 decades ago
quite tricky.........
Teja said:
2 decades ago
hi, i can't understand with ur explanation...
Chetan said:
2 decades ago
i think our problem is to place hindi books in shelf not adjacently but not place english books in middle of hindi books
((( it may look same but just think twice or thrice ...))))
H E H E H E H E H
IF u go in this method the answer will boe aprropriate....
to know the main imp difference btwn permu..and combs visit the link below..
((( it may look same but just think twice or thrice ...))))
H E H E H E H E H
IF u go in this method the answer will boe aprropriate....
to know the main imp difference btwn permu..and combs visit the link below..
Prachi D said:
2 decades ago
somehow i really m not convinced with the explanation, i can have a case where there are two english books separating the two hindi books , meaning
HEEH, like this can be the case as we have more english books than hindi books, please let me know if i am missing out some important information hidden in the problem
HEEH, like this can be the case as we have more english books than hindi books, please let me know if i am missing out some important information hidden in the problem
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