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.
Advertisements
उत्तर
Two coplanar lines that are not parallel intersect each other in a point.
There are 20 straight lines, no two of them 'are parallel and no three of them are concurrent.
So, the number of points of intersection
= 20C2
= `(20!)/((20 - 2)!2!)`
= `(20!)/(18!2!)`
= `(20 xx 19xx18!)/(2xx1xx18!)`
= 190
APPEARS IN
संबंधित प्रश्न
Determine n if `""^(2n)C_3 : ""^nC_3 = 12 : 1`
How many three-digit numbers are there?
How many different numbers of six digits each can be formed from the digits 4, 5, 6, 7, 8, 9 when repetition of digits is not allowed?
f 24Cx = 24C2x + 3, find x.
If α = mC2, then find the value of αC2.
From a group of 15 cricket players, a team of 11 players is to be chosen. In how many ways can this be done?
In how many ways can a football team of 11 players be selected from 16 players? How many of these will
exclude 2 particular players?
There are 10 professors and 20 students out of whom a committee of 2 professors and 3 students is to be formed. Find the number of ways in which this can be done. Further find in how many of these committees:
a particular student is included.
A group consists of 4 girls and 7 boys. In how many ways can a team of 5 members be selected if the team has (i) no girl?
Find the number of ways of selecting 9 balls from 6 red balls, 5 white balls and 5 blue balls if each selection consists of 3 balls of each colour.
Out of 18 points in a plane, no three are in the same straight line except five points which are collinear. How many (ii) triangles can be formed by joining them?
If C (n, 12) = C (n, 8), then C (22, n) is equal to
There are 12 points in a plane. The number of the straight lines joining any two of them when 3 of them are collinear, is
If C0 + C1 + C2 + ... + Cn = 256, then 2nC2 is equal to
Find the number of ways of drawing 9 balls from a bag that has 6 red balls, 5 green balls, and 7 blue balls so that 3 balls of every colour are drawn.
In how many ways a committee consisting of 3 men and 2 women, can be chosen from 7 men and 5 women?
A bag contains six white marbles and five red marbles. Find the number of ways in which four marbles can be drawn from the bag if two must be white and two red
If nC12 = nC8, then n is equal to ______.
A badminton club has 10 couples as members. They meet to organise a mixed double match. If each wife refers to p artner as well as oppose her husband in the match, then the number of different ways can the match off will be ______.
There are 12 persons seated in a line. Number of ways in which 3 persons can be selected such that atleast two of them are consecutive, is ______.
