Advertisements
Advertisements
Question
There are 12 points in a plane of which 5 points are collinear, then the number of lines obtained by joining these points in pairs is 12C2 – 5C2.
Options
True
False
Advertisements
Solution
This statement is False.
Explanation:
Required number of lines = 12C2 – 5C2 + 1
APPEARS IN
RELATED QUESTIONS
If nC8 = nC2, find nC2.
How many chords can be drawn through 21 points on a circle?
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.
In how many ways can one select a cricket team of eleven from 17 players in which only 5 players can bowl if each cricket team of 11 must include exactly 4 bowlers?
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?
Compute:
L.C.M. (6!, 7!, 8!)
Prove that
A coin is tossed five times and outcomes are recorded. How many possible outcomes are there?
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?
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?
How many different numbers of six digits can be formed from the digits 3, 1, 7, 0, 9, 5 when repetition of digits is not allowed?
Evaluate the following:
35C35
If 2nC3 : nC2 = 44 : 3, find n.
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 student choose 5 courses out of 9 courses if 2 courses are compulsory for every student?
How many different selections of 4 books can be made from 10 different books, if
there is no restriction;
Find the number of diagonals of , 1.a hexagon
How many triangles can be obtained by joining 12 points, five of which are collinear?
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?
Find the number of (i) diagonals
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?
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?
5C1 + 5C2 + 5C3 + 5C4 +5C5 is equal to
If 43Cr − 6 = 43C3r + 1 , then the value of r is
Find n if `""^6"P"_2 = "n" ""^6"C"_2`
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.
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?
The value of `(""^9"C"_0 + ""^9"C"_1) + (""^9"C"_1 + ""^9"C"_2) + ... + (""^9"C"_8 + ""^9"C"_9)` is ______
The number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines is ______.
If some or all of n objects are taken at a time, the number of combinations is 2n – 1.
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.
There are 3 books on Mathematics, 4 on Physics and 5 on English. How many different collections can be made such that each collection consists of:
| C1 | C2 |
| (a) One book of each subject; | (i) 3968 |
| (b) At least one book of each subject: | (ii) 60 |
| (c) At least one book of English: | (iii) 3255 |
The number of positive integers satisfying the inequality `""^(n+1)C_(n-2) - ""^(n+1)C_(n-1) ≤ 100` is ______.
There are (n + 1) white and (n + 1) black balls each set numbered 1 to (n + 1). The number of ways in which the balls can be arranged in row so that the adjacent balls are of different colours is ______.
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 ______.

