Advertisements
Advertisements
प्रश्न
There are 11 points in a plane. No three of these lies in the same straight line except 4 points, which are collinear. Find, the number of straight lines that can be obtained from the pairs of these points?
उत्तर
Number of points in a plane = 11
No three of these points lie in the same straight line except 4 points.
The number of straight lines that can be obtained from the pairs of these points
Through any two points, we can draw a straight line.
∴ The number straight lines through any two points of the given 11 points = 11C2
= `(11!)/(2! xx (11 - 2)!)`
= `(11!)/(2! xx 9!)`
= `(11 xx 10 xx 9!)/(2! xx 9!)`
= `(11 xx 10)/(2 xx 1)`
= 11 × 5
= 55
Given that 4 points are collinear.
The number of straight lines through any two points of these 4 points is
= 4C2
= `(4!)/(2!(4 - 2)!)`
= `(4!)/(2! xx 2!)`
= `(4 xx 3xx2!)/(2! xx 2!)`
= `(4 xx 3)/(2 xx 1)`
= 2 × 3
= 6
Since these 4 points are collinear
These 4 points contribute only one line instead of the 6 lines.
The total number of straight lines that can be drawn through 11 points on a plane with 4 of the points being collinear is
= 55 – 6 + 1
= 50
APPEARS IN
संबंधित प्रश्न
There are 18 guests at a dinner party. They have to sit 9 guests on either side of a long table, three particular persons decide to sit on one side and two others on the other side. In how many ways can the guests to be seated?
In how many ways can a cricket team of 11 players be chosen out of a batch of 15 players?
- There is no restriction on the selection.
- A particular player is always chosen.
- A particular player is never chosen.
If nC3 = nC2 then the value of nC4 is:
The number of ways selecting 4 players out of 5 is
If nPr = 720(nCr), then r is equal to:
The number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines is:
Thirteen guests have participated in a dinner. The number of handshakes that happened in the dinner is:
Prove that `""^(2"n")"C"_"n" = (2^"n" xx 1 xx 3 xx ... (2"n" - 1))/("n"!)`
There are 5 teachers and 20 students. Out of them a committee of 2 teachers and 3 students is to be formed. Find the number of ways in which this can be done. Further find in how many of these committees a particular student is excluded?
A committee of 7 peoples has to be formed from 8 men and 4 women. In how many ways can this be done when the committee consists of exactly 3 women?
A committee of 7 peoples has to be formed from 8 men and 4 women. In how many ways can this be done when the committee consists of at least 3 women?
A box contains two white balls, three black balls and four red balls. In how many ways can three balls be drawn from the box, if at least one black ball is to be included in the draw?
How many triangles can be formed by joining 15 points on the plane, in which no line joining any three points?
How many triangles can be formed by 15 points, in which 7 of them lie on one line and the remaining 8 on another parallel line?
Choose the correct alternative:
The number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines
Choose the correct alternative:
Number of sides of a polygon having 44 diagonals is ______
Choose the correct alternative:
`""^(("n" - 1))"C"_"r" + ""^(("n" - 1))"C"_(("r" - 1))` is
Choose the correct alternative:
The product of first n odd natural numbers equals
