The word MATHEMATICS consist of 11 letters:
(M,M), (A,A), (T,T), H,E,I,C,S
Case 1: In this case 2 similar and 2 similar letters are selected, number of arrangements
= 3C2 × \(\frac{4!}{2!\space2!}=756\)
Case 2: In this case all 4 letters selected are different, number of arrangements = 8C4 × 4!
= 1680
Therefore, total number of arrangement = 18 + 756 + 1680
= 2454