Question
How many words can be formed by using the letters of the word ‘ORIENTAL’ so that A and E always occupy the odd places?
Solution
Number of letters in word 'ORIENTAL' = 8 (all distinct)
Number of letters to be used = 8
Step I: A and E are to occupy odd places marked X
Number of letters = 2 (A and E)
Number of boxes = 4
n = 4, r = 2
Number of permutations of arranging A and E = 
...(i)
Step II: After A and E are fixed, there will be 6 letters left and 6 boxes for them.
(A and E use up two boxes)
Number of permutations of arrranging the remaining letters =
...(ii)
Hence, from (i) and (ii), the total number of words formed = 12 x 720 = 8640.
