Advertisements
Advertisements
Question
There are 10 points in a plane of which 4 are collinear. How many different straight lines can be drawn by joining these points.
Advertisements
Solution
Number of straight lines formed joining the 10 points, taking 2 points at a time =
∴ Required number of straight lines =\[45 - 6 + 1 = 40\]
APPEARS IN
RELATED QUESTIONS
If nC8 = nC2, find nC2.
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?
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?
Compute:
(i)\[\frac{30!}{28!}\]
Compute:
L.C.M. (6!, 7!, 8!)
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 team consists of 6 boys and 4 girls and other has 5 boys and 3 girls. How many single matches can be arranged between the two teams when a boy plays against a boy and a girl plays against a girl?
From among the 36 teachers in a college, one principal, one vice-principal and the teacher-incharge are to be appointed. In how many ways can this be done?
How many 9-digit numbers of different digits can be formed?
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?
Evaluate the following:
n + 1Cn
If nC10 = nC12, find 23Cn.
If 28C2r : 24C2r − 4 = 225 : 11, find r.
How many different products can be obtained by multiplying two or more of the numbers 3, 5, 7, 11 (without repetition)?
How many different selections of 4 books can be made from 10 different books, if
there is no restriction;
Determine the number of 5 cards combinations out of a deck of 52 cards if at least one of the 5 cards has to be a king?
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.
A bag contains 5 black and 6 red balls. Determine the number of ways in which 2 black and 3 red balls can be selected.
A parallelogram is cut by two sets of m lines parallel to its sides. Find the number of parallelograms thus formed.
How many words can be formed by taking 4 letters at a time from the letters of the word 'MORADABAD'?
If mC1 = nC2 , then
Given 11 points, of which 5 lie on one circle, other than these 5, no 4 lie on one circle. Then the number of circles that can be drawn so that each contains at least 3 of the given points is
Find n and r if `""^"n""P"_"r"` = 720 and `""^"n""C"_("n" - "r")` = 120
Four parallel lines intersect another set of five parallel lines. Find the number of distinct parallelograms that can be formed.
The value of `(""^9"C"_0 + ""^9"C"_1) + (""^9"C"_1 + ""^9"C"_2) + ... + (""^9"C"_8 + ""^9"C"_9)` is ______
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?
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 can be of any colour
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.
In how many ways can a football team of 11 players be selected from 16 players? How many of them will include 2 particular players?
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.
There are 15 players in a cricket team, out of which 6 are bowlers, 7 are batsmen and 2 are wicketkeepers. The number of ways, a team of 11 players be selected from them so as to include at least 4 bowlers, 5 batsmen and 1 wicketkeeper, is ______.
If number of arrangements of letters of the word "DHARAMSHALA" taken all at a time so that no two alike letters appear together is (4a.5b.6c.7d), (where a, b, c, d ∈ N), then a + b + c + d is equal to ______.
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 ______.
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 ______.
Total number of 6-digit numbers in which only and all the five digits 1, 3, 5, 7 and 9 appear is ______.
