0 votes 0 votes 9 different books are to be arranged on a bookshelf. 4 of these books were written by Shakespeare, 2 by Dickens, and 3 by Conrad. How many possible permutations are there if the books by Conrad must be separated from one another? Combinatory engineering-mathematics discrete-mathematics combinatory + – Lakshman Bhaiya asked Oct 30, 2018 Lakshman Bhaiya 1.7k views answer comment Share Follow See all 5 Comments See all 5 5 Comments reply Mk Utkarsh commented Oct 30, 2018 reply Follow Share Hint : Place 6 books then choose gaps between the books and also both ends to place 3 books by conrad. Then permute 1 votes 1 votes Soumya Tiwari commented Oct 30, 2018 i edited by Soumya Tiwari Oct 30, 2018 reply Follow Share 9!-7!*3! PS: I realized this won't work as in this case all 3 will not be together but 2 Conrad books will be together so we need to place 6 books first and then place 3 books in 7 position so 7P3 *6!*3! leads to correct solution 1 votes 1 votes Gurdeep Saini commented Oct 30, 2018 reply Follow Share @saumya now arrange those 3 book in 3! ways ,you did not arrange them 1 votes 1 votes Gurdeep Saini commented Jan 1, 2019 reply Follow Share @Soumya Tiwari in place of P is should be C ?? 0 votes 0 votes toxicdesire commented Jun 27, 2019 reply Follow Share Assuming + means possible positions for Conrad. The arrangements will be like - + _ + _ + _ + _ + _ + _ + Arrange $6$ books (4 Shakespeare and 2 Dickens) in $6$ places $\implies$ $6!$ Arrange $3$ books in $7$ possible places $\implies$ $^{7}P_{3}$. Thus, total permutations $= \space ^7P_{3} \cdot 6! = 151200$ 1 votes 1 votes Please log in or register to add a comment.
2 votes 2 votes 6 books arrange themselves in 6! ways 3 conard book arange in 3! ways placing 3 books in 6+1(other end) 7c3*6!*3! Cyberspam answered Oct 30, 2018 Cyberspam comment Share Follow See all 0 reply Please log in or register to add a comment.
0 votes 0 votes Arrange 6 books (4 Shakespeare and 2 Dickens) in 6 places =6! now we will see there is 7 place in which we can put 3 books at 7 places=7P3 so answer is 7P3*6! Gurdeep Saini answered Jul 3, 2019 Gurdeep Saini comment Share Follow See all 0 reply Please log in or register to add a comment.