SATHEE: Permutations And Combinations Question 355

Permutations And Combinations Question 355

Question: Consider n points in a plane no three of which are collinear and the ratio of number of hexagon and octagon that can be formed from these n points is 4:13 then find the value of n.

Options:

A) 14

B) 20

C) 28

D) None of these

Show Answer

Answer:

Correct Answer: B

Solution:

[b] From n points number of hexagon is $ ^{n}C_6=\frac{n!}{{(n-6)!}{6!}} $ From n points numbers of octagons is $ ^{n}C_8=\frac{n!}{{(n-8)!}{8!}} $ Ratio of number of hexagon to number of octagon is $ \frac{{(n-8)!}{8!}}{{(n-6)!}{6!}}=\frac{7\times 8}{(n-7)(n-6)}=\frac{4}{13} $ On solving this quadratic equation we will get $ n=20 $

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Permutations And Combinations Question 355

Question: Consider n points in a plane no three of which are collinear and the ratio of number of hexagon and octagon that can be formed from these n points is 4:13 then find the value of n.

Options:

Answer:

Solution:

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