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
Determine the number of 5 card combinations out of a deck of 52 cards if there is exactly one ace in each combination.
If the different permutations of all the letter of the word EXAMINATION are listed as in a dictionary, how many words are there in this list before the first word starting with E?
A coin is tossed five times and outcomes are recorded. How many possible outcomes are there?
How many different five-digit number licence plates can be made if
the first-digit cannot be zero, but the repetition of digits is allowed?
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?
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:
12C10
If nC4 = nC6, find 12Cn.
If 18Cx = 18Cx + 2, find x.
If 8Cr − 7C3 = 7C2, find r.
If n +2C8 : n − 2P4 = 57 : 16, find n.
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 two particular books are never selected?
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.
There are 10 points in a plane of which 4 are collinear. How many different straight lines can be drawn by joining these points.
Determine the number of 5 cards combinations out of a deck of 52 cards if there is exactly one ace in each combination.
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?
If 20Cr = 20Cr + 4 , then rC3 is equal to
If 20Cr + 1 = 20Cr − 1 , then r is equal to
Find the value of 15C4
Find the value of 20C16 – 19C16
Answer the following:
A question paper has 6 questions. How many ways does a student have to answer if he wants to solve at least one question?
In how many ways can the letters of the word 'IMAGE' be arranged so that the vowels should always occupy odd places?
In how many ways a committee consisting of 3 men and 2 women, can be chosen from 7 men and 5 women?
If nCr – 1 = 36, nCr = 84 and nCr + 1 = 126, then find rC2.
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 convex polygon has 44 diagonals. Find the number of its sides.
A group consists of 4 girls and 7 boys. In how many ways can a team of 5 members be selected if the team has no girls
If nC12 = nC8, then n is equal to ______.
Total number of words formed by 2 vowels and 3 consonants taken from 4 vowels and 5 consonants is equal to ______.
Everybody in a room shakes hands with everybody else. The total number of handshakes is 66. The total number of persons in the room is ______.
Three balls are drawn from a bag containing 5 red, 4 white and 3 black balls. The number of ways in which this can be done if at least 2 are red is ______.
The value of `""^50"C"_4 + sum_("r" = 1)^6 ""^(56 - "r")"C"_3` is ______.
A scientific committee is to be formed from 6 Indians and 8 foreigners, which includes at least 2 Indians and double the number of foreigners as Indians. Then the number of ways, the committee can be formed is ______.
If number of arrangements of letters of the word "DHARAMSHALA" taken all at a time so that no two alike letters appear together is (4a.5b.6c.7d), (where a, b, c, d ∈ N), then a + b + c + d is equal to ______.
