Advertisements
Advertisements
प्रश्न
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
उत्तर
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
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.
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?
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?
There are four parcels and five post-offices. In how many different ways can the parcels be sent by registered post?
In how many ways can an examinee answer a set of ten true/false type questions?
How many three-digit numbers are there with no digit repeated?
How many three-digit odd numbers are there?
Since the number has to be greater than 8000, the thousand's place can be filled by only two digits, i.e. 8 and 9.
Now, the hundred's place can be filled with the remaining 4 digits as the repetition of the digits is not allowed.
The ten's place can be filled with the remaining 3 digits.
The unit's place can be filled with the remaining 2 digits.
Total numbers that can be formed = `2xx4xx3xx2=48`
Evaluate the following:
n + 1Cn
If 18Cx = 18Cx + 2, find x.
If 15C3r = 15Cr + 3, find r.
If 15Cr : 15Cr − 1 = 11 : 5, find r.
If n +2C8 : n − 2P4 = 57 : 16, find n.
If 16Cr = 16Cr + 2, find rC4.
A sports team of 11 students is to be constituted, choosing at least 5 from class XI and at least 5 from class XII. If there are 20 students in each of these classes, in how many ways can the teams be constituted?
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 (i) diagonals
Find the number of (ii) triangles
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.
If 20Cr + 1 = 20Cr − 1 , then r is equal to
If nC12 = nC8 , then n =
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
There are 10 points in a plane and 4 of them are collinear. The number of straight lines joining any two of them is
Find the value of 15C4
All the letters of the word ‘EAMCOT’ are arranged in different possible ways. The number of such arrangements in which no two vowels are adjacent to each other is ______.
How many committee of five persons with a chairperson can be selected from 12 persons.
If nCr – 1 = 36, nCr = 84 and nCr + 1 = 126, then find rC2.
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?
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 ______.
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.
There are 10 professors and 20 lecturers out of whom a committee of 2 professors and 3 lecturer is to be formed. Find:
| C1 | C2 |
| (a) In how many ways committee: can be formed | (i) 10C2 × 19C3 |
| (b) In how many ways a particular: professor is included | (ii) 10C2 × 19C2 |
| (c) In how many ways a particular: lecturer is included | (iii) 9C1 × 20C3 |
| (d) In how many ways a particular: lecturer is excluded | (iv) 10C2 × 20C3 |
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 ______.
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 (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 ______.
From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on the shelf so that the dictionary is always in the middle. Then, the number of such arrangements is ______.
A regular polygon has 20 sides. The number of triangles that can be drawn by using the vertices but not using the sides is
