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 A) The number of permutations containing the word RAAT is B) The number of pe

Question

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

A) The number of permutations containing the word RAAT is

B) The number of permutations in which S occurs in the first place and R occurs in the last place is

C) The number of permutations in which none of the letters S, T, R occur in the first 7 positions is

D) The number of permutations in which the letters A, S, R occur in even positions is

Column – II

p) $\frac{7 !}{3 ! 2 !} \times (2)^{4}$

q) $\frac{11 !}{4 ! 3 ! 2 !} \times (2)^{2}$

r) $\frac{11 !}{3 ! 2 !}$

s) $\frac{12 !}{2 !} \times (4)^{4}$

TestHub · Accepted Answer

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 the first position and R in the last position, the remaining 12 letters can be arranged in the remaining 12 positions in $\frac{12 !}{2 ! \times 4 !}$ ways.

C) The first 7 positions can be filled with A, A, A, E, E, M, B, L in $\frac{7 !}{2 ! \times 2 !}$ ways. The remaining 7 positions can be filled with S, S, S, T, T, R, R in $\frac{7 !}{3 ! \times 2 ! \times 2 !}$ ways.

D) The 7 even positions can be filled with A, A, A, S, S, R, R in $\frac{7 !}{2 ! \times 3 ! \times 2 !}$ ways. The 7 odd positions can be filled with T, T, E, E, M, B, L in $\frac{7 !}{2 ! \times 2 !}$ ways.

Mathematics - Permutation & Combination Question with Solution | TestHub

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