Ask Questions, Get Answers

Want to ask us a question? Click here
Browse Questions
Home  >>  CBSE XI  >>  Math  >>  Permutations and Combinations
0 votes

The number of triangles whose vertices are at the vertices of an octagon but none of whose sides happen to come from the octagon is

$\begin{array}{1 1}(A)\;16\\(B)\;28\\(C)\;56\\(D)\;70\end{array} $

Can you answer this question?

1 Answer

0 votes
  • $C(n,r)=\large\frac{n!}{r!(n-r)!}$
Required number of triangles =total number of triangles-number of triangles having two sides common -number of triangles having one side common
$\Rightarrow 8C_3-8-8\times 4$
$\Rightarrow \large\frac{8!}{3!5!}$$-8-8\times 4$
$\Rightarrow \large\frac{8\times 7\times 6\times 5!}{3\times 2\times5!}$$-8-32$
$\Rightarrow 56-8-32$
$\Rightarrow 56-40$
$\Rightarrow 16$
Hence (A) is the correct answer.
answered Jun 20, 2014 by sreemathi.v

Related questions

Ask Question
student study plans
JEE MAIN, CBSE, NEET Mobile and Tablet App
The ultimate mobile app to help you crack your examinations
Get the Android App