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  • If a denotes the number of permutations of x+2 things taken all at a time, b the number of permutations of x things taken 11 at a time and c the number of permutations of x-11 things take

If a denotes the number of permutations of x+2 things taken all at a time, b the number of permutations of x things taken 11 at a time and c the number of permutations of x-11 things taken all at a time such that a=182 b c, then the value of x is

 

Option: 1

15


Option: 2

12


Option: 3

10

 


Option: 4

18


Answers (1)

best_answer

\begin{aligned} & { }^{x+2} P_{x+2}=a \Rightarrow a=(x+2) ! \\ & { }^x P_{11}=b \Rightarrow b=\frac{x !}{(x-11) !} \\ & \text { and } \quad {}^{x-11} P_{x-11}=c \Rightarrow c=(x-11) \text { ! } \\ & \therefore \quad a=182 b c \\ & (x+2) !=182 \frac{x !}{(x-11) !}(x-11) ! \\ & \end{aligned}
\begin{aligned} \Rightarrow & & (x+2)(x+1)=182=14 \times 13 \\ \therefore & & x+1 =13 \\ \therefore & & x =12 \end{aligned}

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