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 618 views comment Share Follow See all 16 Comments See all 16 16 Comments reply Show 13 previous comments 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.