Advertisements
Advertisements
Question
Find the number of diagonals of an n-sided polygon. In particular, find the number of diagonals when n = 8
Solution
There are n vertices in the polygon of n-sides.
If we join any two vertices, we get either side or the diagonal of the polygon.
Two vertices can be joined in nC2 ways.
∴ total number of sides and diagonals = nC2
But there are n sides in the polygon.
∴ total number of the diagonals = nC2 – n
n = 8 sides
∴ the number of diagonals that can be drawn
= 8C2 – 8
= `(8!)/(2!6!) - 8`
= `(8 xx 7 xx 6!)/(2 xx 6!) - 8`
= 28 – 8
= 20
APPEARS IN
RELATED QUESTIONS
Find the value of 15C4
Find the value of `""^80"C"_2`
Find n if `""^"n""C"_("n" - 3)` = 84
Find n and r if `""^"n""C"_("r" - 1): ""^"n""C"_"r": ""^"n""C"_("r" + 1)` = 20:35:42
If `""^"n""P"_"r" = 1814400` and `""^"n""C"_"r"` = 45, find r.
After a meeting, every participant shakes hands with every other participants. If the number of handshakes is 66, find the number of participants in the meeting.
Ten points are plotted on a plane. Find the number of straight lines obtained by joining these points if no three points are collinear.
Ten points are plotted on a plane. Find the number of straight lines obtained by joining these points if four points are collinear.
Find n if `""^"n""C"_8 = ""^"n""C"_12`
Find n, if `""^23"C"_(3"n") = ""^23"C"_(2"n" + 3)`
find the value of `sum_("r" = 1)^4 ""^(21 - "r")"C"_4 + ""^17"C"_5`
Find the differences between the largest values in the following: `""^14"C"_r "and" ""^12"C"_r`
In how many ways can a boy invite his 5 friends to a party so that at least three join the party?
A group consists of 9 men and 6 women. A team of 6 is to be selected. How many of possible selections will have at least 3 women?
A question paper has two sections. section I has 5 questions and section II has 6 questions. A student must answer at least two questions from each section among 6 questions he answers. How many different choices does the student have in choosing questions?
Find n and r if nCr–1 : nCr : nCr+1 = 20 : 35 : 42
Find the number of ways of drawing 9 balls from a bag that has 6 red balls, 8 green balls, and 7 blue balls so that 3 balls of every colour are drawn
After a meeting, every participant shakes hands with every other participants. If the number of handshakes is 66, find the number of participants in the meeting.
Find the number of diagonals of an n-sided polygon. In particular, find the number of diagonals when n = 15
Ten points are plotted on a plane. Find the number of straight lines obtained by joining these points if four points are collinear
Find n if nCn–2 = 15
Find the value of `sum_("r" = 1)^4 ""^((21 - "r"))"C"_4`
Find the differences between the greatest values in the following:
13Cr and 8Cr
In how many ways can a boy invite his 5 friends to a party so that at least three join the party?
A group consists of 9 men and 6 women. A team of 6 is to be selected. How many of possible selections will have at least 3 women?
Answer the following:
A student finds 7 books of his interest but can borrow only three books. He wants to borrow the Chemistry part-II book only if Chemistry Part-I can also be borrowed. Find the number of ways he can choose three books that he wants to borrow.
Answer the following:
There are 4 doctors and 8 lawyers in a panel. Find the number of ways for selecting a team of 6 if at least one doctor must be in the team
The maximum value of z = 9x + 11y subject to 3x + 2y ≤ 12, 2x + 3y ≤ 12, x ≥ 0, y ≥ 0 is _______.
If vertices of a parallelogram are respectively (2, 2), (3, 2), (4, 4), and (3, 4), then the angle between diagonals is ______
In how many ways can a group of 5 boys and 6 girls be formed out of 10 boys and 11 girls?
What is the probability of getting a “FULL HOUSE” in five cards drawn in a poker game from a standard pack of 52-cards?
[A FULL HOUSE consists of 3 cards of the same kind (eg, 3 Kings) and 2 cards of another kind (eg, 2 Aces)]
