Consider all possible permutations of the letters of the word MAST E R B L A S T E R S

14 Letters of the word MASTER BLASTERS are A,A,S,S,S,T,T,E,E,R,R,M,B,L
A) Consider RAAT as one unit. No. of ways of arranging this unit and remaining 10 letters S,S,S,T,E,E,R,M,B,L in a row $=\frac{\lfloor 11}{\lfloor 3\cdot 2}(\because 3\text{ Ss are }$similar, 2Es are similar)

B) After arranging one S in first place, and one R in last place, the number of ways of arranging remaining
12 letters

S,S,A,A,E,E,T,T,R,M,B,L $=\frac{\underset{\_}{2}}{\left(\lfloor 2{)}^4\right.}$

C) A,A,R,R,M,B,L can be arranged in first 7 positions in  $\left(\frac{\angle 7}{\angle 2.\angle 2}\right)$ ways. Now S,S,S,T,T,R,R can be arranged in
last 7 positions in  $\left(\frac{\angle 7}{\angle 3.\angle 2.\angle 2}\right)$ ways. Hence total no. of
arrangements = $\left(\frac{\angle 7}{\angle 2.\angle 2}\times \frac{\angle 7}{\angle 3.\angle 2.\angle 2}\right)=\frac{{\left(\angle 7\right)}^2}{\angle 3.{\left(\angle 2\right)}^4}$

D) No. of ways of arranging 7 letters A,A,S,S,S,R,R in 7 even positions $\left(\frac{\angle 7}{\angle 3.\angle 2.\angle 2}\right)$ 

$\therefore$ Total no. of arrangements $\frac{\angle 7}{\angle 3.\angle 2.\angle 2}\times \frac{\angle 7}{\angle 2.\angle 2}=\frac{{\left(\angle 7\right)}^2}{\angle 3.{\left(\angle 2\right)}^4}$