Question

How many wasy can 8 books, each covering a different subject, be arranged on a shelf such that books on biology, history and programming are never together?

Answer 1

By multiplication rule

number of ways 8 books can be rearraged = 8! = 40320

Let the history biology and programming book are always together and are one book

so now there are 6 books that can be arranged in 6! ways = 720

number of ways these 3 books can be arranged internally = 3*2*1=6

total number of ways these 8 books can be rearranged so that biology. history and programming books are together = 720 * 6 = 4320

This implies that

Number of ways these 8 books can be arrranged such that that books on biology, history and programming are never together = 40320 - 4320 = 36000

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