Advertisements
Advertisements
प्रश्न
Find the number of triangles formed by joining 12 points if four points are collinear.
उत्तर
There are 12 points 1n a plane of which four points are collinear.
If no three points are collinear, we will get 1003 triangles. Since four points are collinear, the number of triangles will reduce by 403.
∴ The number of triangles formed
= `""^12"C"_3 - ""^4"C"_3`
= `220 - (4 xx 3 xx 2)/(3 xx 2)`
= 220 – 4
= 216
APPEARS IN
संबंधित प्रश्न
Find n if `""^"n""C"_("n" - 3)` = 84
Find the number of diagonals of an n-shaded polygon. In particular, find the number of diagonals when: n = 15
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.
Find x if `""^"n""P"_"r" = "x" ""^"n""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 and r if nCr–1 : nCr : nCr+1 = 20 : 35 : 42
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-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 = 8
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 2 vowels are chosen?
Find n if 21C6n = `""^21"C"_(("n"^2 + 5))`
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?
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 arrangements of the letters of the word BANANA in which two N's do not appear adjacently
A student passes an examination if he secures a minimum in each of the 7 subjects. Find the number of ways a student can fail.
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
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 ______.
