Q57 / 160 · TS EAMCET 2024 (09 May Shift 2) · Mathematics

If the number of circular permutations of 9 distinct things taken 5 at a time is $n_1$ and the number of linear permutations of 8 distinct things taken 4 at a time is $n_2$, then $\frac{n_1}{n_2}=$

  • A
    $\frac{5}{9}$
  • B
    2
  • C
    $\frac{1}{2}$
  • Correct answer
    D
    $\frac{9}{5}$

Solution

$n_1=$ number of circular permutations of 9 distinct taken 5 at a time $={ }^9 C_5 \cdot 4!$ $n_2=$ number of linear permutation of 8 distinct things taken 4 at a time $={ }^8 C_4 \cdot 4$ ? $\therefore \frac{n_1}{n_2}=\frac{{ }^9 C_5 \cdot 4!}{{ }^8 C_4 \cdot 4!}=\frac{9!}{5!4!} \times \frac{4!4!}{8!}=\frac{9}{5}$

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

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