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 2 of 3.
Saurabh said:
1 decade ago
So I think 23c19 is the better choice. And I think the arrangement of the english or hindi books within themselves doesn't matter according to question. Please reply for the choice between 22c19 or 23c19.
Vishal said:
2 decades ago
Sambit. Great explanation.
Thanks.
Thanks.
Priti said:
2 decades ago
Hi.
What is means the 22c19 & 22c3 ?.
What is means the 22c19 & 22c3 ?.
Mohan said:
2 decades ago
Gaurav is right
21P21 * 22P19
21P21 * 22P19
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?
Gaurav said:
2 decades ago
Assuming all the books are distinct:
22 places for 19 hindi books so 22P19 ways.
English books can be arranged within themselves in 21P21=21! ways.
so total ways = 22P19 * 21P21
22 places for 19 hindi books so 22P19 ways.
English books can be arranged within themselves in 21P21=21! ways.
so total ways = 22P19 * 21P21
Tarun said:
2 decades ago
ok try this one
lets we take english books as E
and we have 21 English books
so let they are placed like this
EEEEEEEEEEEEEEEEEEEEE
and 19 hindi books
now let hindi books as H
now find out total places in above self so that two hindi books never be together
so you can place hindi books on '-' only ,like
-E-E-E-E-E-E-E-E-E-E-E-E-E-E-E-E-E-E-E-E-E- .......(1)
f;e
HE H EE H EH EH E E HE HE HE HE HE HE HE HE HE HE HE HE HE HE
or
EH EH EH EH EH EH EH EH E E HE HE HE H EE H EH EH EH EH EH EH
both are correct,there are some Englidh books together also,
but notice one thing H is always place on a '-' its up to u use any '-'
so if you count there are 22 '-' in eq 1
and you can place 19 Hindi books on any of these 22 '-'
so we have to fill only 19 '-' out of 22 '-'
so use formula given in first explanation its correct
lets we take english books as E
and we have 21 English books
so let they are placed like this
EEEEEEEEEEEEEEEEEEEEE
and 19 hindi books
now let hindi books as H
now find out total places in above self so that two hindi books never be together
so you can place hindi books on '-' only ,like
-E-E-E-E-E-E-E-E-E-E-E-E-E-E-E-E-E-E-E-E-E- .......(1)
f;e
HE H EE H EH EH E E HE HE HE HE HE HE HE HE HE HE HE HE HE HE
or
EH EH EH EH EH EH EH EH E E HE HE HE H EE H EH EH EH EH EH EH
both are correct,there are some Englidh books together also,
but notice one thing H is always place on a '-' its up to u use any '-'
so if you count there are 22 '-' in eq 1
and you can place 19 Hindi books on any of these 22 '-'
so we have to fill only 19 '-' out of 22 '-'
so use formula given in first explanation its correct
Sambit said:
2 decades ago
Don't we need the arrangement here? Let us consider that there were 5 English books and 3 Hindi books. We have 6 places where we can place the Hindi books so that they are not together.
1 E 2 E 3 E 4 E 5 E 6
But, we need 3 places. So, we can choose 3 out of 6 places in 6C3 ways. But, then we can also arrange the 3 books in 3! i.e 6 ways. So, the total number of ways in which we can place/arrange the books is 6C3 * 3!, which is also same as 6P3 (The definition of Permutation says that you choose r objects out of n objects and then arrange these r objects). And also the 5 English books can be arranged in 5! ways, which will again result in a different arrangement. So, total ways of placing both the English and Hindi books would be 6P3 * 5!. Am i right or did i make a mistake in understanding the question?
1 E 2 E 3 E 4 E 5 E 6
But, we need 3 places. So, we can choose 3 out of 6 places in 6C3 ways. But, then we can also arrange the 3 books in 3! i.e 6 ways. So, the total number of ways in which we can place/arrange the books is 6C3 * 3!, which is also same as 6P3 (The definition of Permutation says that you choose r objects out of n objects and then arrange these r objects). And also the 5 English books can be arranged in 5! ways, which will again result in a different arrangement. So, total ways of placing both the English and Hindi books would be 6P3 * 5!. Am i right or did i make a mistake in understanding the question?
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
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..
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