Match the following: Consider all possible permutations of the letters of the word 

M A S T E R B L A S T E R S

	Column-I		Column-II
A)	The number of permutations containing the word RAAT is	P)	$\frac{{(7!)}^2}{3!{(2!)}^4}$
B)	The number of permutations in which S occurs in first place and R occurs in the last place is	Q)	$\frac{11!\times 4!}{3!\times {(2!)}^2}$
C)	The number of permutations in which none of the letters S, T, R occur in first 7 positions is	R)	$\frac{11!}{3!\times 2!}$
D)	The number of permutations in which the letters A, S, R occur in even positions  is	S)	$\frac{12!}{{(2!)}^4}$

 

 AA, SSS, TT, EE, RR, M, B, L 

A) Take RAAT as one unit.  Therefore 10 + 1 = 11 units can be arranged in $\frac{11!}{3!\times 2!}$ ways.

B) After fixing S in first position  and R in last position  the remaining 12 letters can be arranged in  remaining  12 positions  in $\frac{12!}{{(2!)}^4}$ ways

C) First 7 positions can be filled with $A\text{'}s,E\text{'}s,M,B,Lin\frac{7!}{{(2!)}^2}$ ways. The remaining 7 positions can be filled with $S\text{'}s,T\text{'}s,R\text{'}sin\frac{7!}{3!\times {(2!)}^2}$ ways.

D) 7 even positions  can be filled with $A\text{'}s,S\text{'}s,R\text{'}sin\frac{7!}{{(2!)}^2\times 3!}$ ways. 7 odd positions  can be filled with $T\text{'}s,E\text{'}s,M,B,Lin\frac{7!}{{(2!)}^2}$