The total number of ways of formation of five letter words from the letters of t

The word INDEPENDENT has letters: I(1), N(3), D(2), E(3), P(1), T(1). To form 5-letter words, we consider cases based on repetition patterns. Cases: all distinct (6 choose 5 * 5! = 720), one pair (3 choices for pair, choose 3 other distinct from 5, 30 selections * 60 permutations = 1800), two pairs (3 choices for two pairs, 4 choices for fifth, 12 selections * 30 permutations = 360), three of a kind (2 choices for triple, choose 2 other distinct from 5, 20 selections * 20 permutations = 400), full house (3 of a kind and a pair: 4 selections * 10 permutations = 40). Total = 720+1800+360+400+40 = 3320.