We define a bow-tie quadrilateral as a quadrilateral where two sides cross each other. An example of a bow-tie quadrilateral is shown below. Seven distinct points are chosen on a circle. We draw all $\binom{7}{2} = 21$ chords that connect two of these points. Four of these $21$ chords are selected at random. What is the probability that these four chosen chords form a bow-tie quadrilateral?

Step-by-step explanation:

Suppose we choose four points on the circle. Then there are exactly two ways that they can form the vertices of a bow-tie.

[there is an image below]

Thus, there are exactly 2 times 7c4 = 70 bow-tie quadrilaterals that can be formed among the seven points.

There are 21 chords to choose from, so there are 21c4 = 5985 ways to choose four chords. Therefore, the probability that the four chords form a bow-tie quadrilateral is

70/5985 = 2/171.

solution:

→c= a b , that is product of a and b is possible only when when a is m × n matrix and b is n × p matrix.

that is, number of columns of a= number of rows of b.

so, size of matrix , c= a b is , if a = (m × n)matrix

b= (n × p)matrix

then a b = [ (m × n)matrix] ×[   (n × p)matrix ]

→→c= a b= [m × p ] matrix

→→size of product a b will be equal to = number of rows of a × number of columns of b