1 votes 1 votes Find the number of ways to distribute 10 books in 3 shelves. I considered it as an ordered problem which is fully unspecified. So, answer should be 310. But the given answer is 12P2. Where am i going wrong? Combinatory combinatory discrete-mathematics + – Nymeria asked Jan 19, 2018 edited Jan 19, 2018 by srestha Nymeria 399 views answer comment Share Follow See all 3 Comments See all 3 3 Comments reply MiNiPanda commented Jan 19, 2018 i edited by MiNiPanda Jan 19, 2018 reply Follow Share If the books are distinct then can't we apply (n+r-1,n-1)? And if they are identical then..I have a doubt what will be the answer.. Anu007 Sir please help.. 1 votes 1 votes Nymeria commented Jan 19, 2018 reply Follow Share Pigeonhole principle can help you find atleast how many books go to the same shelf. Here, on the other hand, we have to find total ways. 0 votes 0 votes MiNiPanda commented Jan 19, 2018 reply Follow Share Sorry..I confused it with something different.. I meant that (n+r-1)C(n-1) ..using this formula.. I edited that .. Thanks.. 0 votes 0 votes Please log in or register to add a comment.
1 votes 1 votes THere would be two cases:- CASE!:- if all the books are distimct then it would be ... 103 case2:- if all the books r identical then.... coefficient of x10 in (1+x+x2+x3+......+x10)3 ....10+3-1C10 ->12C2 hs_yadav answered Jan 19, 2018 hs_yadav comment Share Follow See all 3 Comments See all 3 3 Comments reply Nymeria commented Jan 19, 2018 i edited by Nymeria Jan 19, 2018 reply Follow Share Oh got it! Thank you. But here the question doesn't explicitly specify anything. Is that the reason we have taken case 2? In case "distinct" is mentioned, then only should we go for case 1? Also in case 1 shouldn't it be 3^10? 0 votes 0 votes hs_yadav commented Jan 19, 2018 reply Follow Share yes ...i think so 0 votes 0 votes Nymeria commented Jan 19, 2018 reply Follow Share Thank you. 0 votes 0 votes Please log in or register to add a comment.