If ^ 56 P_ r + 6 :^ 54 P_ r + 3 = 30800:1, then r = - Vidyadip

MCQ

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

A
$31$
✓
$41$
C
$51$
D
None of these

✓

Answer

Correct option: B.

$41$

b
(b) $\frac{{56\;!}}{{(50 - r)\;!}} \times \frac{{(51 - r)\;!}}{{54\;!}}$

$ = \frac{{30800}}{1} \Rightarrow 56 \times 55 \times (51 - r) = 30800$

$ \Rightarrow $ $r = 41$.

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