Find the number of ways in which n books on mathematics and n books on chemistry can be placed alternatively on a shelf.
Total number of books = n + n = 2n
Let the places on the shelf for these books are: 1, 2, 3, 4, 5, 6, ..........(2n - 3), (2n - 2), (2n - 1), 2n.
M C M C M C M C M C
Case (i)
Mathematics books are arranged on odd number places and chemistry books are placed on even number places.
Number of arrangements =
Or
Case (ii)
Chemistry books are placed an odd number places and mathematics books on even number places.
Number of arrangements =
Hence, the total number of arrangements on the shelf where mathematics books and chemistry books are placed alternatively.