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