Advertisements
Advertisements
प्रश्न
Find the number of diagonals of (ii) a polygon of 16 sides.
Advertisements
उत्तर
A polygon of n sides has n vertices. By joining any two vertices we obtain either a side or a diagonal.
∴ Number of ways of selecting 2 out of 9 \[=^n C_2 = \frac{n\left( n - 1 \right)}{2}\]
Out of these lines, n lines are the sides of the polygon.
∴ Number of diagonals =\[\frac{n\left( n - 1 \right)}{2} - n = \frac{n\left( n - 3 \right)}{2}\]
There are 16 sides.
∴ Number of diagonals =\[\frac{16\left( 16 - 3 \right)}{2} = 104\]
APPEARS IN
संबंधित प्रश्न
How many chords can be drawn through 21 points on a circle?
In how many ways can one select a cricket team of eleven from 17 players in which only 5 players can bowl if each cricket team of 11 must include exactly 4 bowlers?
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?
How many 6-digit numbers can be formed from the digits 0, 1, 3, 5, 7 and 9 which are divisible by 10 and no digit is repeated?
Compute:
(i)\[\frac{30!}{28!}\]
Compute:
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 coin is tossed five times and outcomes are recorded. How many possible outcomes are there?
How many A.P.'s with 10 terms are there whose first term is in the set {1, 2, 3} and whose common difference is in the set {1, 2, 3, 4, 5}?
How many three-digit odd numbers are there?
How many 9-digit numbers of different digits can be formed?
How many different numbers of six digits can be formed from the digits 3, 1, 7, 0, 9, 5 when repetition of digits is not allowed?
Evaluate the following:
14C3
Evaluate the following:
12C10
Evaluate the following:
35C35
If nC10 = nC12, find 23Cn.
In how many ways can a student choose 5 courses out of 9 courses if 2 courses are compulsory for every student?
In how many ways can a football team of 11 players be selected from 16 players? How many of these will
exclude 2 particular players?
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.
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 student is excluded.
How many different selections of 4 books can be made from 10 different books, if two particular books are never selected?
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.
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. In how many ways can he choose the 7 questions?
There are 10 points in a plane of which 4 are collinear. How many different straight lines can be drawn by joining these points.
A committee of 3 persons is to be constituted from a group of 2 men and 3 women. In how many ways can this be done? How many of these committees would consist of 1 man and 2 women?
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: atmost 3 girls?
How many words can be formed by taking 4 letters at a time from the letters of the word 'MORADABAD'?
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?
A tea party is arranged for 16 persons along two sides of a long table with 8 chairs on each side. Four persons wish to sit on one particular side and two on the other side. In how many ways can they be seated?
If 20Cr + 1 = 20Cr − 1 , then r is equal to
There are 12 points in a plane. The number of the straight lines joining any two of them when 3 of them are collinear, is
There are 10 points in a plane and 4 of them are collinear. The number of straight lines joining any two of them is
Among 14 players, 5 are bowlers. In how many ways a team of 11 may be formed with at least 4 bowlers?
In how many ways a committee consisting of 3 men and 2 women, can be chosen from 7 men and 5 women?
In how many ways can a football team of 11 players be selected from 16 players? How many of them will exclude 2 particular players?
Given 5 different green dyes, four different blue dyes and three different red dyes, the number of combinations of dyes which can be chosen taking at least one green and one blue dye is ______.
There are 3 books on Mathematics, 4 on Physics and 5 on English. How many different collections can be made such that each collection consists of:
| C1 | C2 |
| (a) One book of each subject; | (i) 3968 |
| (b) At least one book of each subject: | (ii) 60 |
| (c) At least one book of English: | (iii) 3255 |
The number of positive integers satisfying the inequality `""^(n+1)C_(n-2) - ""^(n+1)C_(n-1) ≤ 100` is ______.
