Also note that number of words formed using EEEEI will be 5!/ 4! As it has 5 words with E repeating 4 times. Corresponding to each of these arrangements, the 5 vowels E, E, E, E and I can be rearranged in
5!/ 4! Ways.
Therefore, by multiplication principle the required number of arrangements is 8!/( 3! 2!) * 5!/ 4! = 16800
( iii) To find number of words where vowels never occur together, let’ s find total number of possible words & then subtract the words where vowel occur together.
Total number of words with 12 letters where N appears 3 times, E appears 4 times and D appears 2 times and the rest are all different is 12!/( 3! * 2! * 4!) = 1663200
Total number of words with vowels not together = 1663200 – 16800 = 1646400
( iv) If we fix I and P at the extreme ends( I at the left end and P at the right end). We are left with 10 letters, where N appears 3 times, E appears 4 times and D appears 2 times and the rest are all different is
Hence, the required number of arrangements is 10!/( 3! * 2! * 4!) = 12600
Combination: Combination means selection of things. Order of things has no importance. Eg; Select 2 players from a pool of 3 players