First slide

Combinations

Question

There are n concurrent lines and another line parallel to one of them. The number of different triangles that will be formed by the (n + 1) lines, is

Moderate

A

$\frac{(n - 1) n}{2}$
B

$\frac{(n - 1) (n - 2)}{2}$
C

$\frac{n (n + 1)}{2}$
D

$\frac{(n + 1) (n + 2)}{2}$

Solution

The number of triangles = number of selections of 2 lines from the (n – 1) lines which are cut by the last line
$=^{n - 1} C_{2} = \frac{(n - 1)!}{2! (n - 3)!} = \frac{(n - 1) (n - 2)}{2}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App