Question

If there are 15 distinct points on a plane what is the maximum no of straight lines

Answer 1

Given,

there are 15 distinct points.

We know that a point can be observed by joining two points.

We have to choose 2 points from collection of 15 points

So,

Numbers of ways to choose 2 points will be = $^{15}C_2 \\ \\ = \frac{15!}{(15-2)! \ 2!} \\ \\ = \frac{15!}{13! \ 2!} \\ \\ = \frac{15*14}{2} \\ \\ = 15*7 \\ \\ = 105$

Answer 2

Answer: The total number of straight lines is 105.

Step-by-step explanation:   Given that there are 15 distinct points in the plane. For one straight line, we need to join two points. Of course, this is a problem of permutation and combination.

Since the direction of the straight line does not matter here, so we will use the formula for combination, i.e., combination of 15 points taking 2 at a time.

Therefore, the total number of lines is given by

$\dfrac{15!}{2!(15-2)!}\\\\\\=\dfrac{15!}{2!13!}\\\\=\dfrac{15\times 14\times 13!}{2\times 1\times 13!}\\\\\\=\dfrac{15\times 14}{2\times 1}\\\\=7\times 15\\=105.$

Thus, the answer is 105.