Advertisements
Advertisements
प्रश्न
How many triangles can be formed by joining 15 points on the plane, in which no line joining any three points?
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.
Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?
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.
Let there be 3 red, 2 yellow and 2 green signal flags. How many different signals are possible if we wish to make signals by arranging all of them vertically on a staff?
If nC3 = nC2 then the value of nC4 is:
The number of ways selecting 4 players out of 5 is
The number of diagonals in a polygon of n sides is equal to
The value of (5C0 + 5C1) + (5C1 + 5C2) + (5C2 + 5C3) + (5C3 + 5C4) + (5C4 + 5C5) is:
A Kabaddi coach has 14 players ready to play. How many different teams of 7 players could the coach put on the court?
How many chords can be drawn through 20 points on a circle?
Find the total number of subsets of a set with
[Hint: nC0 + nC1 + nC2 + ... + nCn = 2n] 5 elements
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?
How many different selections of 5 books can be made from 12 different books if, Two particular books are always selected?
Determine the number of 5 card combinations out of a deck of 52 cards if there is exactly three aces in each combination
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?
Choose the correct alternative:
Number of sides of a polygon having 44 diagonals is ______
Choose the correct alternative:
In 2nC3 : nC3 = 11 : 1 then
Choose the correct alternative:
The number of ways of choosing 5 cards out of a deck of 52 cards which include at least one king is
