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.
Mohan said:
2 decades ago
I think the answer is wrong. The solution only provides the count on the number of ways hindi books can be arranged in a row so that two hindi books are never together. It doesn't consider the number of ways the english books can be arranged between them.
To further elaborate.
----------------------
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. :)
I feel the solution to this problem
No of ways 22 eng books can be arranged * No of ways 19 books can be arranged in 22 slots
= 21! * 22C19
HAPPY CALCULATING...
To further elaborate.
----------------------
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. :)
I feel the solution to this problem
No of ways 22 eng books can be arranged * No of ways 19 books can be arranged in 22 slots
= 21! * 22C19
HAPPY CALCULATING...
Mahanthesh naik said:
9 years ago
Correct ans is= 22c19 * 21! *19!.
Jyothi said:
10 years ago
ncr = nc(n-r) so 22c19 = 22c(22-19) which is 22c3.
Mansi said:
1 decade ago
Why are we not calculating the ways to arrange English books by doing 19?
Sreeejith said:
1 decade ago
Hey guys I have hit the wall with the same question Is it permutation or combination?
Somia said:
1 decade ago
The total no.of arrangements that can be made by the word rainbow are:
7! = 5040 words.
Let us consider, the "row" as a single letter so now the remaining letters are "ainb" four letters, then it is total a 5 letter word,
The no. of ways for the five letter words are ways, 5! ways = 120 words. And it remains same for bow.
Am I correct please correct me if I am wrong?
7! = 5040 words.
Let us consider, the "row" as a single letter so now the remaining letters are "ainb" four letters, then it is total a 5 letter word,
The no. of ways for the five letter words are ways, 5! ways = 120 words. And it remains same for bow.
Am I correct please correct me if I am wrong?
NISHA said:
1 decade ago
Find the number of words that can be formed by using all the letters of the word RAINBOW.
How many of them end ROW and BOW?
How many of them end ROW and BOW?
Preeti said:
1 decade ago
Yes, the question is about arrangement and the solution given is the combination of Hindi books, the selection is done in 22C19 ways but what about arranging them?
Himaja said:
1 decade ago
21c19 is the way of choosing the places for 19 hindi books, but what about arranging them?, according to me I thought that 21c19 is the way to choose places and 19p19 for arranging them. Can anyone say is this right or wrong, please.
Saurav said:
1 decade ago
The solution for this question will be 22C19. Because it is question related to combination because all the book of english are identicals. No need to take 21!.
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