Advertisements
Advertisements
प्रश्न
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
उत्तर
There are 20 lines such that no two of them are parallel and no three of them are concurrent.
Since no two lines are parallel
∴ they intersect at a point
∴ Number of points of intersection if no two lines are parallel and no three lines are concurrent
= 20C2
= `(20!)/(2!18!)`
= `(20 xx 19 xx 18!)/(2 xx 1 xx 18!)`
= 190
APPEARS IN
संबंधित प्रश्न
Find the value of `""^80"C"_2`
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 20 points are marked on a circle, how many chords can be drawn?
Find n, if `""^23"C"_(3"n") = ""^23"C"_(2"n" + 3)`
Find n, if `""^21"C"_(6"n") = ""^21"C"_(("n"^2 + 5)`
Find n, if `""^"n""C"_("n" - 2)` = 15
Find x if `""^"n""P"_"r" = "x" ""^"n""C"_"r"`
find the value of `sum_("r" = 1)^4 ""^(21 - "r")"C"_4 + ""^17"C"_5`
In how many ways can a boy invite his 5 friends to a party so that at least three join the party?
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 questions from each section among 6 questions he answers. How many different choices does the student have in choosing questions?
Find n and r if nCr–1 : nCr : nCr+1 = 20 : 35 : 42
If nPr = 1814400 and nCr = 45, find n+4Cr+3
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 = 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
Find n if nC8 = nC12
Find n if 23C3n = 23C2n+3
Find n if 2nCr–1 = 2nCr+1
Find n if nCn–2 = 15
Find r if 11C4 + 11C5 + 12C6 + 13C7 = 14Cr
Find the differences between the greatest values in the following:
13Cr and 8Cr
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?
There are 3 wicketkeepers and 5 bowlers among 22 cricket players. A team of 11 players is to be selected so that there is exactly one wicketkeeper and at least 4 bowlers in the team. How many different teams can be formed?
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
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
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:
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.
Answer the following:
Find the number of ways of dividing 20 objects in three groups of sizes 8, 7 and 5
If `1/(8!) + 1/(7!) = x/(9!)`, than x is equal to ______.
If 'n' is positive integer and three consecutive coefficient in the expansion of (1 + x)n are in the ratio 6 : 33 : 110, then n is equal to ______.
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 ______.
