@saumya

now arrange those 3 book in 3! ways ,you did not arrange them

now arrange those 3 book in 3! ways ,you did not arrange them

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Lakshman Patel RJIT
asked
in Combinatory
Oct 30, 2018

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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?

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

+ _ + _ + _ + _ + _ + _ +

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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