Q74 / 180 · COMEDK 2014 · Mathematics

If ${ }^{56} P_{r+6}:{ }^{54} P_{r+3}=30800: 1$, then

  • Correct answer
    A
    $r=41$
  • B
    $r=51$
  • C
    $r=31$
  • D
    None of these

Solution

Given, ${ }^{56} P_{r+6}:^{54} P_{r+3}=30800: 1$ $\Rightarrow \quad \frac{{ }^{56} P_{r+6}}{{ }^{54} P_{r+3}}=\frac{30800}{1}$ $\Rightarrow \quad \frac{56 ! \times(51-r) !}{(50-r) ! \times 54 !}=\frac{30800}{1}$ $\Rightarrow 56 \times 55 \times(51-r)=30800$ $\Rightarrow \quad 51-r=10 \Rightarrow r=41$

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

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