Question

The number of ways in which four letters can be selected from the letters of the word "MATHEMATICS" is

• A. $133$
• B. $146$
• C. $136$
• D. $73$

Answer 1

The correct option is C $136$

The word MATHEMATICS has $2$ M's, $2$ A's, $2$ T's and H,E,I,C,S
The total number of selection $=$ (All different $+2$ alike, $2$ different $+2$ alike $2$ other alike)
$=$ $\left(\begin{array}{c}8\\ 4\end{array}\right)+\left(\begin{array}{c}3\\ 2\end{array}\right)+\left(\begin{array}{c}3\\ 1\end{array}\right)\left(\begin{array}{c}7\\ 2\end{array}\right)=136$