Advertisements
Advertisements
प्रश्न
How many triangles can be formed by joining 15 points on the plane, in which no line joining any three points?
Advertisements
उत्तर
Number of points 15
To form a triangle we need 3 non-collinear points.
The number of ways of selecting 3 non-collinear points from 15 points is = 15C3
= `(15!)/(3!(15 - 3)!)`
= `(15!)/(3! 2!)`
= `(15 xx 14 xx 13 xx 12!)/(3 xx 2!)`
= `(15 xx 14 xx 1)/(3 xx 2 xx 1)`
= 5 × 7 × 13
= 455
APPEARS IN
संबंधित प्रश्न
Verify that 8C4 + 8C3 = 9C4.
How many chords can be drawn through 21 points on a circle?
How many triangles can be formed by joining the vertices of a hexagon?
From 20 raffle tickets in a hat, four tickets are to be selected in order. The holder of the first ticket wins a car, the second a motor cycle, the third a bicycle and the fourth a skateboard. In how many different ways can these prizes be awarded?
Thirteen guests have participated in a dinner. The number of handshakes that happened in the dinner is:
If `""^(("n" + 1))"C"_8 : ""^(("n" - 3))"P"_4` = 57 : 16, find the value of n
There are 15 persons in a party and if each 2 of them shakes hands with each other, how many handshakes happen in the party?
How many chords can be drawn through 20 points on a circle?
A trust has 25 members. How many ways 3 officers can be selected?
A trust has 25 members. In how many ways can a President, Vice President and a Secretary be selected?
How many ways a committee of six persons from 10 persons can be chosen along with a chair person and a secretary?
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?
In an examination a student has to answer 5 questions, out of 9 questions in which 2 are compulsory. In how many ways a student can answer the questions?
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 most 3 women?
Find the number of strings of 4 letters that can be formed with the letters of the word EXAMINATION?
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?
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?
There are 11 points in a plane. No three of these lie in the same straight line except 4 points which are collinear. Find the number of triangles that can be formed for which the points are their vertices?
