The number of 5-letter words, with or without meaning, that can be formed using the letters of the word ASSASSINATION such that the first and the last letters are identical is _ _ _ _ _ _ .

Step-by-step solution

The word ASSASSINATION consists of 13 letters with the following frequencies: S(4), A(3), I(2), N(2), T(1), O(1). There are 6 distinct letters. Let the 5-letter word be of the form X _ _ _ X . The letter X must have a frequency of at least 2 in the original word, so X can be S, A, I, or N. We must choose and arrange 3 letters for the middle positions from the remaining multiset after removing two instances of X . Case 1: X = S Remaining letters: S(2), A(3), I(2), N(2), T(1), O(1). (6 distinct letters) - 3 distinct