If 56 P r + 6 : 54 P r + 3 = 30800:1, then r = Options: A . &nbsp 31 B . &nbsp 41 C . &nbsp 51 D . &nbsp 40

Answer: Option B : B 56 ! ( 50 − r ) ! × ( 51 − r ) ! 54 ! = 30800 1 ⇒ 56 × 55 × ( 51 − r ) = 30800 ⇒ r = 41

If 56Pr+6:54Pr+3 = 30800:1, then r =

Question

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

Options:

A . 31

B . 41

C . 51

D . 40

Answer: Option 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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