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9 different books are to be arranged on a book-shelf. 4 of these books were written by Shakespeare, 2 by Dickens and 3 by Conrad. How many possible permutations are there if

(c) the books by Conrad are separated from each other?

Note by Daniel Kua
1 year, 10 months ago

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Hi Daniel,

To answer your question, first of all we notice that order matters. The 6 Shakespeare and Dickens books (denoted by "O" below) can be put down in \(6!=720\) ways. We then have 7 possible places to put the Conrad books down (on either side of the "O's"). Each Conrad book at a different X-spot however because the Conrad books need to be separated from each other.

X O X O X O X O X O X O X

As there are 7 possible places for the 1st Conrad book, 6 possible places for the 2nd Conrad book and 5 possible places for the 3rd Conrad book, the total number of permutations is \(6! \times 7 \times 6 \times 5 = 151200\).

Kind regards,

Patrick Heebels

Patrick Heebels - 1 year, 8 months ago

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May be....plz let me know the ans

Shreya Patel - 1 year, 10 months ago

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210

Shreya Patel - 1 year, 10 months ago

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no. the answer is 151200.

Daniel Kua - 1 year, 9 months ago

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