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 3 of 3.
Pallavi said:
2 decades ago
quite tricky.........
Phanindra said:
2 decades ago
Why he begin arrangment with hindi book? and how he got the 22 places?
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.
Ananth said:
2 decades ago
Hi Nikhil,
nCr = nC (n-r).
nCr = nC (n-r).
Yog said:
2 decades ago
What is the difference between permutation and combination?
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.
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?
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