0 votes 0 votes closed as a duplicate of: MadeEasy Subject Test 2019: Combinatory - Permutations And Combinations Number of ways we can arrange 5 books in 3 selves___________ Combinatory combinatory + – srestha asked Jan 31, 2019 • closed Jan 31, 2019 by Shaik Masthan srestha 662 views comment Share Follow See all 16 Comments See all 16 16 Comments reply Mk Utkarsh commented Jan 31, 2019 reply Follow Share Depends on books, identical or distinct 0 votes 0 votes sreenivas.s1995 commented Jan 31, 2019 reply Follow Share https://gateoverflow.in/300636/madeeasy?show=300881 0 votes 0 votes Shaik Masthan commented Jan 31, 2019 reply Follow Share update the test series name in the Title ! @srestha 0 votes 0 votes Magma commented Jan 31, 2019 reply Follow Share I'M not open that link But I try to explain it in my way 5 books 3 selves 3 selves act as a divide a 5 books / how many ways we can do partition of 5 books It can be 4 | 1| 0 or 5 | 0 | 0 or 2 | 2 | 1 etc etc Now, if we want to divide 4 chocolate among 3 children --> 2 sticks needed for partition right ??? Now , same in this scenario think like we want to distribute 5 books among 3 children, so here we also need 2 partitions $\binom{5+2}{2}$ Now we're just partitioning it , but question is we can arrange 5 books in 3 selves Now we should arrange it by = $\binom{5+2}{2} X 5!$ = $\frac{7!}{2!}$ 2 votes 2 votes Shaik Masthan commented Jan 31, 2019 reply Follow Share i don't know why you don't have the powers of "EDITOR" after getting BOSS tag ? @magma 0 votes 0 votes Mk Utkarsh commented Jan 31, 2019 reply Follow Share no relation :p 0 votes 0 votes Mk Utkarsh commented Jan 31, 2019 reply Follow Share Magma if you want to become editor you have to mail to gatecse 0 votes 0 votes Magma commented Jan 31, 2019 reply Follow Share Dunno @Shaik Masthan brother :( 0 votes 0 votes Shaik Masthan commented Jan 31, 2019 reply Follow Share in case of me, after attaining the BOSS tag, my privileges increases ! i thought there is a relation between them ! ( either you have >10k points or >365 days journey ) @Mk Utkarsh 0 votes 0 votes Mk Utkarsh commented Jan 31, 2019 reply Follow Share Shaik Masthan AFAIK there is no relation, i got 10k long back but i became editor few months ago 0 votes 0 votes srestha commented Jan 31, 2019 reply Follow Share @Shaik u already updated with closing madeeasy tag na? otherwise I have to reopen @Magma what should be condition for combination then? 0 votes 0 votes Magma commented Jan 31, 2019 reply Follow Share @srestha mam I didn't get you point ----> "what should be condition for combination then?" 0 votes 0 votes Shaik Masthan commented Jan 31, 2019 reply Follow Share mam, no need right now, but next time on posting of the question should be take care ( i know o need to say to you but still, forgive me if anything wrong ) what should be condition for combination then? i didn't get what it means ? 0 votes 0 votes srestha commented Jan 31, 2019 reply Follow Share @Magma I got ur point actually we are arranging books but not two selves, that is why divide by 2. but how do we know, selves are not distinct like upper selves and lower selves? @Shaik Masthan ok , I never mind :) All the best for GATE to all of u:) 0 votes 0 votes Magma commented Jan 31, 2019 reply Follow Share actually we are arranging books but not two selves, that is why divide by 2. It's not like that 5 books You inserted 2 sticks between 5 books to make a partition of 3 Total elements = 5+2 Now you gave to only 2 students because whatever is left at last is gave to last students Like 2 | 2 | 1 Total 7 elements ( 5 books + 2 sticks ) Distribute to 2 child 1st will get = 2 books 2nd will get = 2 books And we didn't take care for what 3rd student will get Because whatever is left after giving to 1st and 2nd student we will gave it to 3rd student That's why From 7 elements we choose only 2 $\binom{5+2}{2}$ Here all books are different that's why we multiply with 5! If all books are identical than it's = $\binom{5+2}{2} X \frac{5!}{5!}$ " Sticks are only concept that we introduce to simply solve such questions " "If in this question it's given that books selves are also different " Than it has to be = $\binom{5+2}{2} X 5! X 2!$ 0 votes 0 votes srestha commented Jan 31, 2019 reply Follow Share @Magma what will be ans if they ask for "Number of ways we can arrange 5 identical books in 3 children___________" 0 votes 0 votes Please log in or register to add a comment.