Advertisements
Advertisements
प्रश्न
Find the number of diagonals of an n-shaded polygon. In particular, find the number of diagonals when: n = 15
Advertisements
उत्तर
Two points are needed to draw a segment.
A polygon of n sides has n vertices.
So, in a polygon of n sides, there will be
nC2 segments, which include its sides and diagonals both.
Since the polygon has n sides, the number of its diagonals is nC2 – n
Here, n = 15
∴ The number of diagonals = 15C2 – 15
= `(15!)/((15 - 2)!2!) - 15`
= `(15 xx 14)/2 - 15`
= 105 – 15
= 90
APPEARS IN
संबंधित प्रश्न
Find the value of `""^20"C"_16 - ""^19"C"_16`
If `""^"n""P"_"r" = 1814400` and `""^"n""C"_"r"` = 45, find r.
Find the number of ways of selecting a team of 3 boys and 2 girls from 6 boys and 4 girls.
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.
Find the differences between the largest values in the following: `""^14"C"_r "and" ""^12"C"_r`
Find the differences between the largest values in the following: `""^15"C"_r "and" ""^11"C"_r`
In how many ways can a boy invite his 5 friends to a party so that at least three join the party?
Find r if 14C2r : 10C2r–4 = 143 : 10
Find the number of diagonals of an n-sided polygon. In particular, find the number of diagonals when n = 15
There are 20 straight lines in a plane so that no two lines are parallel and no three lines are concurrent. Determine the number of points of intersection
Find the number of triangles formed by joining 12 points if four points are collinear
Find n if nC8 = nC12
Find n if 2nCr–1 = 2nCr+1
Find r if 11C4 + 11C5 + 12C6 + 13C7 = 14Cr
Find the value of `sum_("r" = 1)^4 ""^((21 - "r"))"C"_4`
Find the differences between the greatest values in the following:
14Cr and 12Cr
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 question from each section among 6 questions he answers. How many different choices does the student have in choosing questions?
Answer the following:
30 objects are to be divided in three groups containing 7, 10, 13 objects. Find the number of distinct ways for doing so.
