Question

In how many ways can a pair of parallel diagonals of a regular polygon of 10 sides be
selected?​

Answer 1

Answer:

The answer is 60 pair of parallel diagonals

Answer 2

Answer:

The number of ways a pair of parallel diagonals of regular polygon of 10 sides can be selected is 105

Step-by-step explanation:

Number of diagonals of a n sided regular polygon = n(n - 3)/2

Number of diagonals of a 10 sided regular polygon = 10 × (10 - 3)/2

                                                                                      = 35

For a n sided polygon if n is even then the number of parallel diagonal is given by n(n - 4)/4

Therefore, the number of parallel diagonals in 10 sided regular polygon

= 10(10 - 4)/4 = 60/4 = 15

Therefore, the number of ways to select the pair of parallel diagonals

= ${15}\choose 2$

= $\frac{15!}{13!2!}$

= $\frac{15\times14\times13!}{2!\times13!}$

= 105