Question

The number of $4$ letter words (with or without meaning) that can be made from the eleven letters of the word "EXAMINATION" is

Answer 1

Word "EXAMINATION" consists of 2A, 2I, 2N, E, X, M, T, O
Case I: All different letters are selected
Number of words formed: ${}^8{C}_4\times 4!=1680$
Case II: 2 letters are same and 2 are different
Number of words formed $={}^3{C}_1\times {}^7{C}_2\times \frac{4!}{2!}=756$
Case III: 2 pair of letters are same
Number of words formed $={}^3{C}_2\times \frac{4!}{2!\times 2!}=18$
Total number of words formed $=1680+756+18=2454$