Find the no. of Permutations of all the letters of the word MATHEMATICS which starts with consonants only

A
$\frac{7 \times 10!}{8}$
B
$\frac{11!}{5}$
C
$\frac{10!}{9}$
D
$\frac{10!}{8}$

Solution:

(MM), (AA), (TT), H, E, I, C, S

Words starting with M or T $= \frac{2 \times 10!}{2! 2!}$

Words starting with H, C, S $= \frac{3 x 10!}{2! 2! 2!}$

Hence number of words are

$\begin{array}{l} \frac{2 \times 10!}{2! 2!} + \frac{3 \times 10!}{2! 2! 2!} \\ = \frac{10!}{2} + \frac{3 \times 10!}{8} \\ = \frac{4 \times 10! + 3 \times 10!}{8} \\ = \frac{7 \times 10!}{8} \end{array}$

Solution:

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