Q78 / 160 · AP EAMCET 2023 (18 May Shift 2) · Mathematics

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

  • A
    $\frac{1}{2}$
  • B
    $\frac{5}{16}$
  • Correct answer
    C
    $\frac{2}{19}$
  • D
    $\frac{2}{81}$

Solution

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 $=\frac{18_{\mathrm{C}_6} \times 2 ! \times(13-1) ! \times 6 !}{(20-1) !}=\frac{2}{19}$

Hence, the correct answer is option: 'C'.

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