Advertisements
Advertisements
प्रश्न
Find the number of diagonals of an n-shaded polygon. In particular, find the number of diagonals when: n = 12
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 = 12
∴ The number of diagonals = 12C2 – 12
= `(12!)/((12 - 2)!2!) - 12`
= `(12 xx 11)/2 - 12`
= 66 – 12
= 54
APPEARS IN
संबंधित प्रश्न
Find the value of 15C4
Find the value of `""^15"C"_4 + ""^15"C"_5`
Find n and r if `""^"n""C"_("r" - 1): ""^"n""C"_"r": ""^"n""C"_("r" + 1)` = 20:35:42
If `""^"n""C"_("r" - 1)` = 6435, `""^"n""C"_"r"` = 5005, `""^"n""C"_("r" + 1)` = 3003, find `""^"r""C"_5`.
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.
A word has 8 consonants and 3 vowels. How many distinct words can be formed if 4 consonants and 12 vowels are chosen?
Find n, if `""^23"C"_(3"n") = ""^23"C"_(2"n" + 3)`
Find n, if `""^"n""C"_("n" - 2)` = 15
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 the majority?
If nCr–1 = 6435, nCr = 5005, nCr+1 = 3003, find rC5
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 n if nC8 = nC12
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?
Five students are selected from 11. How many ways can these students be selected if two specified students are not selected?
Select the correct answer from the given alternatives.
A question paper has two parts, A and B, each containing 10 questions. If a student has to choose 8 from part A and 5 from part B, In how many ways can he choose the questions?
Select the correct answer from the given alternatives.
The number of ways in which 5 male and 2 female members of a committee can be seated around a round table so that the two females are not seated together is
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.
In how many ways can a group of 5 boys and 6 girls be formed out of 10 boys and 11 girls?
Out of 7 consonants and 4 vowels, the number of words (not necessarily meaningful) that can be made, each consisting of 3 consonants and 2 vowels, is ______.
