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If $\mathrm{A}$ and $\mathrm{B}$ are among 20 persons who sit at random along a round table, then the probability that there are any six persons between $A$ and $B$ is
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The correct answer is:
$\frac{2}{19}$
The no. of ways in which 18 people (excluding $A$ and $B$ ) sit in a round table with 6 people between $\mathrm{A} \& \mathrm{~B}={ }^{18} \mathrm{C}_6 \times 2 ! \times(13-1)$ !
Thus, probability $=\frac{18_{\mathrm{C}_6} \times 2 ! \times(13-1) ! \times 6 !}{(20-1) !}=\frac{2}{19}$
Thus, probability $=\frac{18_{\mathrm{C}_6} \times 2 ! \times(13-1) ! \times 6 !}{(20-1) !}=\frac{2}{19}$
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