Advertisements
Advertisements
प्रश्न
Find the number of (ii) triangles
Advertisements
उत्तर
(ii) Number of triangles (i.e. 3 sides are to be selected) = \[{}^{10} C_3 = \frac{10}{3} \times \frac{9}{2} \times \frac{8}{1} = 120\]
APPEARS IN
संबंधित प्रश्न
If nC8 = nC2, find nC2.
Determine n if `""^(2n)C_3 : ""^nC_3 = 12 : 1`
How many chords can be drawn through 21 points on a circle?
Determine the number of 5 card combinations out of a deck of 52 cards if there is exactly one ace in each combination.
Given 7 flags of different colours, how many different signals can be generated if a signal requires the use of two flags, one below the other?
How many three-digit numbers are there?
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?
If 15C3r = 15Cr + 3, find r.
There are 10 professors and 20 students out of whom a committee of 2 professors 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 professor is included.
How many different selections of 4 books can be made from 10 different books, if
two particular books are always selected;
From 4 officers and 8 jawans in how many ways can 6 be chosen. to include at least one officer?
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?
In an examination, a student has to answer 4 questions out of 5 questions; questions 1 and 2 are however compulsory. Determine the number of ways in which the student can make the choice.
In how many ways can a team of 3 boys and 3 girls be selected from 5 boys and 4 girls?
Determine the number of 5 cards combinations out of a deck of 52 cards if there is exactly one ace in each combination.
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: exactly 3 girls?
Out of 18 points in a plane, no three are in the same straight line except five points which are collinear. How many (i) straight lines
Find the number of ways in which : (b) an arrangement, of four letters can be made from the letters of the word 'PROPORTION'.
Find the number of combinations and permutations of 4 letters taken from the word 'EXAMINATION'.
If nC12 = nC8 , then n =
Total number of words formed by 2 vowels and 3 consonants taken from 4 vowels and 5 consonants is equal to
In how many ways can a committee of 5 be made out of 6 men and 4 women containing at least one women?
How many different committees of 5 can be formed from 6 men and 4 women on which exact 3 men and 2 women serve?
(a) 6
(b) 20
(c) 60
(d) 120
If 43Cr − 6 = 43C3r + 1 , then the value of r is
The number of diagonals that can be drawn by joining the vertices of an octagon is
Find the number of ways of drawing 9 balls from a bag that has 6 red balls, 5 green balls, and 7 blue balls so that 3 balls of every colour are drawn.
There are 8 doctors and 4 lawyers in a panel. Find the number of ways for selecting a team of 6 if at least one doctor must be in the team.
Find the value of 80C2
The straight lines l1, l2 and l3 are parallel and lie in the same plane. A total numbers of m points are taken on l1; n points on l2, k points on l3. The maximum number of triangles formed with vertices at these points are ______.
There are 10 lamps in a hall. Each one of them can be switched on independently. Find the number of ways in which the hall can be illuminated.
In an examination, a student has to answer 4 questions out of 5 questions; questions 1 and 2 are however compulsory. Determine the number of ways in which the student can make the choice.
The total number of ways in which six ‘+’ and four ‘–’ signs can be arranged in a line such that no two signs ‘–’ occur together is ______.
A candidate is required to answer 7 questions out of 12 questions which are divided into two groups, each containing 6 questions. He is not permitted to attempt more than 5 questions from either group. He can choose the seven questions in 650 ways.
Number of selections of at least one letter from the letters of MATHEMATICS, is ______.
The no. of different ways, the letters of the word KUMARI can be placed in the 8 boxes of the given figure so that no row remains empty will be ______.
