Advertisements
Advertisements
प्रश्न
Find the number of diagonals of an n-shaded polygon. In particular, find the number of diagonals when: n = 10
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 = 10
∴ The number of diagonals = 10C2 – 10
= `(10!)/((10 - 2)!2!) - 10`
= `(10 xx 9)/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`
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-shaded polygon. In particular, find the number of diagonals when: n = 12
Find n, if `""^"n""C"_("n" - 2)` = 15
Find the differences between the largest values in the following: `""^15"C"_r "and" ""^11"C"_r`
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?
Find n if 2nC3 : nC2 = 52 : 3
Find r if 14C2r : 10C2r–4 = 143 : 10
If nPr = 1814400 and nCr = 45, find n+4Cr+3
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 = 10
Find the number of diagonals of an n-sided polygon. In particular, find the number of diagonals when n = 12
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
Ten points are plotted on a plane. Find the number of straight lines obtained by joining these points if four points are collinear
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 not selected?
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
