Question:
how many words can be formed out of the letters of the word ORIENTAL such that A and E occupy odd places?
Answer:
Given word is ORIENTAL
Total letters = 8
Odd places = 4
Even places = 4
Now the letters O, E can be arranged in odd places = 2 * 4C2 = 2 * (4*3)/(2*1) = 2 * 6 = 12 {Multiply by 2 is for AE and EA combinations}
There are 6 places and 6 letters can be placed = 6! = 720
Now, total number of words = 12 * 720 = 8640
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