Advertisements
Advertisements
प्रश्न
Find the number of triangles formed by joining 12 points if no three points are collinear
Advertisements
उत्तर
A triangle can be formed by selecting 3 non-collinear points.
We can choose 3 points from 12 points in
12C3 = `(12!)/(3!9!)`
= `(12 xx 11 xx 10 xx 9!)/(3 xx 2 xx 1 xx 9!)`
= 220 ways
∴ number of triangles = 220.
APPEARS IN
संबंधित प्रश्न
Find n and r if `""^"n""C"_("r" - 1): ""^"n""C"_"r": ""^"n""C"_("r" + 1)` = 20:35:42
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 the number of diagonals of an n-shaded polygon. In particular, find the number of diagonals when: n = 12
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.
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 `""^"n""C"_("n" - 2)` = 15
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: `""^13"C"_r "and" ""^8"C"_r`
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?
Find n if nCn–3 = 84
Find r if 14C2r : 10C2r–4 = 143 : 10
Find n and r if nCr–1 : nCr : nCr+1 = 20 : 35 : 42
If nCr–1 = 6435, nCr = 5005, nCr+1 = 3003, find rC5
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
Find the number of diagonals of an n-sided polygon. In particular, find the number of diagonals when n = 10
Find n if nC8 = nC12
Find n if 21C6n = `""^21"C"_(("n"^2 + 5))`
Find n if 2nCr–1 = 2nCr+1
Find the differences between the greatest values in the following:
14Cr and 12Cr
Find the differences between the greatest values in the following:
13Cr and 8Cr
Find the differences between the greatest values in the following:
15Cr and 11Cr
In how many ways can a boy invite his 5 friends to a party so that at least three join the party?
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?
Five students are selected from 11. How many ways can these students be selected if two specified students are 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
Answer the following:
Four parallel lines intersect another set of five parallel lines. Find the number of distinct parallelograms formed
The maximum value of z = 9x + 11y subject to 3x + 2y ≤ 12, 2x + 3y ≤ 12, x ≥ 0, y ≥ 0 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)]
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 ______.
