Aptitude - Permutation and Combination - Discussion

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?

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

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

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...

Gaurav is right
21P21 * 22P19

Hi.

What is means the 22c19 & 22c3 ?.

Sambit. Great explanation.

Thanks.

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.

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!.

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.