N choose K

Probability Level 2

If n + 2 C 8 : n − 2 P 4 = 57 : 16 ^{n+2}C_{8}:^{n-2}P_4=57:16 ,find n n .


The answer is 19.

Rohit Udaiwal by Rohit Udaiwal , 20, India

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1 solution

Rishabh Jain
Dec 31, 2015

( n + 2 ) ! 8 ! × ( n − 6 ) ! × ( n − 6 ) ! ( n − 2 ) ! = 57 16 \frac {(n+2)!}{8!\times(n-6)!}\times\frac{(n-6)!}{(n-2)!}=\frac{57}{16} ⇒ ( n + 2 ) ( n + 1 ) ( n ) ( n − 1 ) = 57 16 × 8 ! \Rightarrow (n+2)(n+1)(n)(n-1)=\frac {57}{16} \times 8! =21•20•19•18

⇒ n = 19 \Rightarrow n=19

4 Helpful 0 Interesting 0 Brilliant 0 Confused

That's again cool!

Rohit Udaiwal - 5 years, 5 months ago

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Thanks ...... :)

Rishabh Jain - 5 years, 5 months ago

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