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?

Answer 1

There are 4 odd places in the word

∴ Number of permutations = ⁴P₂ = 4!/2! = 12

Now the remaining 6 places filled with remaining 6 letters 

∴ Number of permutations = ⁶P₆ = 6!/0! = 720

Hence the total number of permutations = 12 × 720 = 8640