Advertisements
Advertisements
प्रश्न
Find the number of diagonals of an n-sided polygon. In particular, find the number of diagonals when n = 10
Advertisements
उत्तर
In an n-sided polygon, there are ‘n’ points and ‘n’ sides.
∴ Through ‘n’ points we can draw nC2 lines including sides.
∴ Number of diagonals in n sided polygon
= nC2 – n .........(n = number of sides)
n = 10
nC2 – n = 10C2 – 10
= `(10 xx 9)/(1 xx 2) - 10`
= 45 – 10
= 35
APPEARS IN
संबंधित प्रश्न
Find the value of 15C4
Find the value of `""^80"C"_2`
Find the value of `""^20"C"_16 - ""^19"C"_16`
Find r if `""^14"C"_(2"r"): ""^10"C"_(2"r" - 4)` = 143:10
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.
If `""^"n""C"_("r" - 1)` = 6435, `""^"n""C"_"r"` = 5005, `""^"n""C"_("r" + 1)` = 3003, find `""^"r""C"_5`.
If 20 points are marked on a circle, how many chords can be drawn?
Find the number of diagonals of an n-shaded polygon. In particular, find the number of diagonals when: n = 15
Find n, if `""^21"C"_(6"n") = ""^21"C"_(("n"^2 + 5)`
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 nPr = 720 and nCn–r = 120
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.
If 20 points are marked on a circle, how many chords can be drawn?
Find the number of diagonals of an n-sided polygon. In particular, find the number of diagonals when n = 15
Find n if 21C6n = `""^21"C"_(("n"^2 + 5))`
Find r if 11C4 + 11C5 + 12C6 + 13C7 = 14Cr
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 committee of 10 persons is to be formed from a group of 10 women and 8 men. How many possible committees will have at least 5 women? How many possible committees will have men in majority?
A question paper has two sections. section I has 5 questions and section II has 6 questions. A student must answer at least two question from each section among 6 questions he answers. How many different choices does the student have in choosing questions?
Five students are selected from 11. How many ways can these students be selected if two specified students are selected?
Answer the following:
Ten students are to be selected for a project from a class of 30 students. There are 4 students who want to be together either in the project or not in the project. Find the number of possible selections
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:
Nine friends decide to go for a picnic in two groups. One group decides to go by car and the other group decides to go by train. Find the number of different ways of doing so if there must be at least 3 friends in each group.
Answer the following:
Find the number of ways of dividing 20 objects in three groups of sizes 8, 7 and 5
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
Answer the following:
Four parallel lines intersect another set of five parallel lines. Find the number of distinct parallelograms formed
If vertices of a parallelogram are respectively (2, 2), (3, 2), (4, 4), and (3, 4), then the angle between diagonals is ______
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)]
