Aclassic counting problem is to determine the number of different ways that the letters of "occasionally" can be arranged. find that number.

The word has 12 letters in total, distributed as follows:

2 o's
2 c's
2 a's
1 s
1 i
1 n
2 l's
1 y.

There are permutations of 12 objects. Nevertheless, since we have repeating letters, swapping them would still return the same words.

So, the new total is

Answer with explanation:

⇒Number of Alphabets in the word " OCCASIONALLY"

                              = 12

⇒Combination of Alphabets in  word " OCCASIONALLY"

     =  O---2, C--2, A--2,S---1, I---1, N---1, L---2, Y----1

⇒Number of ways by which Letters of Word  " OCCASIONALLY" can be Arranged, as order of Alphabets is also Important,So we will use the concept of Permutation.Also, letter O,C, A and L appear 2 times .So we will divide it to total number of Alphabets taking factorial of each number as well as total number of Alphabets.