1 1 vote 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 1.1k views answer comment Share Follow Print See all 3 Comments 3 3 Comments reply MiNiPanda commented Jan 19, 2018 i edited by MiNiPanda Jan 19, 2018 reply Follow flag 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 1 replyShare Nymeria commented Jan 19, 2018 reply Follow flag 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 0 replyShare MiNiPanda commented Jan 19, 2018 reply Follow flag Sorry..I confused it with something different.. I meant that (n+r-1)C(n-1) ..using this formula.. I edited that .. Thanks.. 0 0 replyShare Please log in or register to add a comment.
1 1 vote 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 3 3 Comments reply Nymeria commented Jan 19, 2018 i edited by Nymeria Jan 19, 2018 reply Follow flag 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 0 replyShare hs_yadav commented Jan 19, 2018 reply Follow flag yes ...i think so 0 0 replyShare Nymeria commented Jan 19, 2018 reply Follow flag Thank you. 0 0 replyShare Please log in or register to add a comment.
