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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?
in Combinatory
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@saumya

now arrange those 3 book in 3! ways ,you did not arrange them
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@Soumya Tiwari in place of P is should be C ??

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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  $= \space  ^7P_{3} \cdot 6! = 151200$
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2 Answers

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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!
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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!