The number of words of 4 letters which can be formed with the letters of the word M A T H E M A T I C S is α , then α 300 is

Step-by-step solution

M , A , T → 2 H , E , I , C , S → 1 Type Combination Permutation all different 8 C 4 8 P 4 = 1680 2 same 2 different 3 C 1 × 7 C 1 3 C 1 × 7 C 1 × 4 ! 2 ! = 756 2 same 2 same 3 C 2 3 C 2 × 4 ! 2 ! = 18 Total number of words = 2454 2454 300 = 8.1 8