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
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 the number of 5 card combinations out of a deck of 52 cards if there is exactly one ace in each combination.
A person wants to buy one fountain pen, one ball pen and one pencil from a stationery shop. If there are 10 fountain pen varieties, 12 ball pen varieties and 5 pencil varieties, in how many ways can he select these articles?
A mint prepares metallic calendars specifying months, dates and days in the form of monthly sheets (one plate for each month). How many types of calendars should it prepare to serve for all the possibilities in future years?
A coin is tossed five times and outcomes are recorded. How many possible outcomes are there?
There are 6 multiple choice questions in an examination. How many sequences of answers are possible, if the first three questions have 4 choices each and the next three have 2 each?
How many three-digit numbers are there with no digit repeated?
In how many ways can six persons be seated in a row?
How many odd numbers less than 1000 can be formed by using the digits 0, 3, 5, 7 when repetition of digits is not allowed?
If nC12 = nC5, find the value of n.
If 8Cr − 7C3 = 7C2, find r.
How many different boat parties of 8, consisting of 5 boys and 3 girls, can be made from 25 boys and 10 girls?
How many different products can be obtained by multiplying two or more of the numbers 3, 5, 7, 11 (without repetition)?
In an examination, a student has to answer 4 questions out of 5 questions; questions 1 and 2 are however compulsory. Determine the number of ways in which the student can make the choice.
In a village, there are 87 families of which 52 families have at most 2 children. In a rural development programme, 20 families are to be helped chosen for assistance, of which at least 18 families must have at most 2 children. In how many ways can the choice be made?
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
Five students are selected from 11. How many ways can these students be selected if two specified students are not selected?
Find the value of 15C4 + 15C5
Answer the following:
A question paper has 6 questions. How many ways does a student have to answer if he wants to solve at least one question?
A candidate is required to answer 7 questions out of 12 questions which are divided into two groups, each containing 6 questions. He is not permitted to attempt more than 5 questions from either group. He can choose the seven questions in 650 ways.
The no. of different ways, the letters of the word KUMARI can be placed in the 8 boxes of the given figure so that no row remains empty will be ______.
