Question

4 points out of 8 points in a place are collinear. Number of different quadrilateral that can be formed by joining them is: a) 56 , b)53 , c)76, d)60

Answer 1

Answer on Question #48802 – Math – Combinatorics | Number Theory

Task:

4 points out of 8 points in a place are collinear. Number of different quadrilateral that can be formed by joining them is:

a) 56

b) 53

c) 76

d) 60

Solution:

We have 4 Collinear points and 4 Others.

We can have 4 of the 4 Others: 1.

We can have 3 Others and 1 Collinear: $C_4^3 C_4^1 = \frac{4!}{3! \cdot 1!} \cdot \frac{4!}{3! \cdot 1!} = 16$

We can have 2 Others and 2 Collinears: $C_4^2 C_4^2 = \frac{4!}{2! \cdot 2!} \cdot \frac{4!}{2! \cdot 2!} = 36$

Therefore, there are: $36 + 16 + 1 = 53$ quadrilaterals.

Answer: b) 53

www.AssignmentExpert.com