Advertisements
Advertisements
प्रश्न
How many chords can be drawn through 21 points on a circle?
Advertisements
उत्तर
For drawing one chord on a circle, only 2 points are required.
To know the number of chords that can be drawn through the given 21 points on a circle, the number of combinations have to be counted.
Therefore, there will be as many chords as there are combinations of 21 points taken 2 at a time.
Thus, required number of chords =
= 21C2 = `(21!)/(2!(21 - 2)!) = (21!)/(2!19!)`
= `(21 xx 20)/(1 xx 2)`
= 210
APPEARS IN
संबंधित प्रश्न
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:
(i) exactly 3 girls?
(ii) atleast 3 girls?
(iii) atmost 3 girls?
Compute:
(i)\[\frac{30!}{28!}\]
A mint prepares metallic calendars specifying months, dates and days in the form of monthly sheets (one plate for each month). How many types of calendars should it prepare to serve for all the possibilities in future years?
A team consists of 6 boys and 4 girls and other has 5 boys and 3 girls. How many single matches can be arranged between the two teams when a boy plays against a boy and a girl plays against a girl?
How many three-digit numbers are there?
How many odd numbers less than 1000 can be formed by using the digits 0, 3, 5, 7 when repetition of digits is not allowed?
Evaluate the following:
n + 1Cn
If 8Cr − 7C3 = 7C2, find r.
If nC4 , nC5 and nC6 are in A.P., then find n.
If α = mC2, then find the value of αC2.
From a group of 15 cricket players, a team of 11 players is to be chosen. In how many ways can this be done?
How many different selections of 4 books can be made from 10 different books, if
there is no restriction;
From 4 officers and 8 jawans in how many ways can 6 be chosen. to include at least one officer?
There are 10 points in a plane of which 4 are collinear. How many different straight lines can be drawn by joining these points.
In how many ways can a committee of 5 persons be formed out of 6 men and 4 women when at least one woman has to be necessarily selected?
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?
A parallelogram is cut by two sets of m lines parallel to its sides. Find the number of parallelograms thus formed.
How many different words, each containing 2 vowels and 3 consonants can be formed with 5 vowels and 17 consonants?
A business man hosts a dinner to 21 guests. He is having 2 round tables which can accommodate 15 and 6 persons each. In how many ways can he arrange the guests?
Write \[\sum^m_{r = 0} \ ^{n + r}{}{C}_r\] in the simplified form.
If mC1 = nC2 , then
If C0 + C1 + C2 + ... + Cn = 256, then 2nC2 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
Ten students are to be selected for a project from a class of 30 students. There are 4 students who want to be together either in the project or not in the project. Find the number of possible selections.
Find the value of 15C4 + 15C5
A boy has 3 library tickets and 8 books of his interest in the library. Of these 8, he does not want to borrow Mathematics Part II, unless Mathematics Part I is also borrowed. In how many ways can he choose the three books to be borrowed?
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 ______.
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 ______.
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 selections be made?
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 number of triangles that are formed by choosing the vertices from a set of 12 points, seven of which lie on the same line is ______.
15C8 + 15C9 – 15C6 – 15C7 = ______.
If some or all of n objects are taken at a time, the number of combinations is 2n – 1.
The number of positive integers satisfying the inequality `""^(n+1)C_(n-2) - ""^(n+1)C_(n-1) ≤ 100` 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 ______.
