Advertisements
Advertisements
प्रश्न
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
विकल्प
62
63
64
65
Advertisements
उत्तर
64
Number of straight lines joining 12 points if we take 2 points at a time = 12C2
\[= \frac{12!}{2! 10!} = 66\]
Number of straight lines joining 3 points if we take 2 points at a time = 3C2 = 3
But, 3 collinear points, when joined in pairs, give only one line.
∴ Required number of straight lines =\[66 - 3 + 1 = 64\]
APPEARS IN
संबंधित प्रश्न
In how many ways can a team of 3 boys and 3 girls be selected from 5 boys and 4 girls?
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.
How many words, with or without meaning, each of 2 vowels and 3 consonants can be formed from the letters of the word DAUGHTER?
How many words, with or without meaning, can be formed using all the letters of the word EQUATION at a time so that the vowels and consonants occur together?
A committee of 7 has to be formed from 9 boys and 4 girls. In how many ways can this be done when the committee consists of:
(i) exactly 3 girls?
(ii) atleast 3 girls?
(iii) atmost 3 girls?
In an examination, a question paper consists of 12 questions divided into two parts i.e., Part I and Part II, containing 5 and 7 questions, respectively. A student is required to attempt 8 questions in all, selecting at least 3 from each part. In how many ways can a student select the questions?
From a class of 25 students, 10 are to be chosen for an excursion party. There are 3 students who decide that either all of them will join or none of them will join. In how many ways can the excursion party be chosen?
A letter lock consists of three rings each marked with 10 different letters. In how many ways it is possible to make an unsuccessful attempt to open the lock?
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?
There are 5 books on Mathematics and 6 books on Physics in a book shop. In how many ways can a students buy : (i) a Mathematics book and a Physics book (ii) either a Mathematics book or a Physics book?
If 15C3r = 15Cr + 3, find r.
If 28C2r : 24C2r − 4 = 225 : 11, find r.
In how many ways can a football team of 11 players be selected from 16 players? How many of these will
include 2 particular players?
From a class of 12 boys and 10 girls, 10 students are to be chosen for a competition; at least including 4 boys and 4 girls. The 2 girls who won the prizes last year should be included. In how many ways can the selection be made?
How many different selections of 4 books can be made from 10 different books, if
two particular books are always selected;
In how many ways can a committee of 5 persons be formed out of 6 men and 4 women when at least one woman has to be necessarily selected?
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 (ii) at least one boy and one girl?
We wish to select 6 persons from 8, but if the person A is chosen, then B must be chosen. In how many ways can the selection be made?
In how many ways can one select a cricket team of eleven from 17 players in which only 5 persons can bowl if each cricket team of 11 must include exactly 4 bowlers?
How many different words, each containing 2 vowels and 3 consonants can be formed with 5 vowels and 17 consonants?
How many words can be formed by taking 4 letters at a time from the letters of the word 'MORADABAD'?
A business man hosts a dinner to 21 guests. He is having 2 round tables which can accommodate 15 and 6 persons each. In how many ways can he arrange the guests?
There are 3 letters and 3 directed envelopes. Write the number of ways in which no letter is put in the correct envelope.
Three persons enter a railway compartment. If there are 5 seats vacant, in how many ways can they take these seats?
In how many ways can a committee of 5 be made out of 6 men and 4 women containing at least one women?
The number of ways in which a host lady can invite for a party of 8 out of 12 people of whom two do not want to attend the party together is
If 43Cr − 6 = 43C3r + 1 , then the value of r is
Find n if `""^6"P"_2 = "n" ""^6"C"_2`
Five students are selected from 11. How many ways can these students be selected if two specified students are not selected?
A student finds 7 books of his interest, but can borrow only three books. He wants to borrow Chemistry part II book only if Chemistry Part I can also be borrowed. Find the number of ways he can choose three books that he wants to borrow.
Four parallel lines intersect another set of five parallel lines. Find the number of distinct parallelograms that can be formed.
A student has to answer 10 questions, choosing atleast 4 from each of Parts A and B. If there are 6 questions in Part A and 7 in Part B, in how many ways can the student choose 10 questions?
In a small village, there are 87 families, of which 52 families have atmost 2 children. In a rural development programme 20 families are to be chosen for assistance, of which atleast 18 families must have at most 2 children. In how many ways can the choice be made?
We wish to select 6 persons from 8, but if the person A is chosen, then B must be chosen. In how many ways can selections be made?
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 they must all be of the same colour.
Everybody in a room shakes hands with everybody else. The total number of handshakes is 66. The total number of persons in the room is ______.
A committee of 6 is to be chosen from 10 men and 7 women so as to contain atleast 3 men and 2 women. In how many different ways can this be done if two particular women refuse to serve on the same committee ______.
All possible numbers are formed using the digits 1, 1, 2, 2, 2, 2, 3, 4, 4 taken all at a time. The number of such numbers in which the odd digits occupy even places is ______.
Number of selections of at least one letter from the letters of MATHEMATICS, is ______.
