Advertisements
Advertisements
प्रश्न
Out of 18 points in a plane, no three are in the same straight line except five points which are collinear. How many (ii) triangles can be formed by joining them?
उत्तर
Number of triangles formed joining the 18 points, taking 3 points at a time =\[{}^{18} C_3 = \frac{18}{3} \times \frac{17}{2} \times \frac{16}{1} = 816\]
Number of straight lines formed joining the 5 points, taking 3 points at a time =\[{}^5 C_3 = \frac{5}{3} \times \frac{4}{2} \times \frac{3}{1} = 10\]
∴ Required number of triangles =\[816 - 10 = 806\]
APPEARS IN
संबंधित प्रश्न
Determine n if `""^(2n)C_3 : ""^nC_3 = 12 : 1`
A bag contains 5 black and 6 red balls. Determine the number of ways in which 2 black and 3 red balls can be selected.
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 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?
How many four digit different numbers, greater than 5000 can be formed with the digits 1, 2, 5, 9, 0 when repetition of digits is not allowed?
f 24Cx = 24C2x + 3, find x.
If nC4 , nC5 and nC6 are in A.P., then find n.
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 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?
In a village, there are 87 families of which 52 families have at most 2 children. In a rural development programme, 20 families are to be helped chosen for assistance, of which at least 18 families must have at most 2 children. In how many ways can the choice be made?
In how many ways can a student choose a programme of 5 courses if 9 courses are available and 2 specific courses are compulsory for every student?
How many words can be formed by taking 4 letters at a time from the letters of the word 'MORADABAD'?
If\[\ ^{( a^2 - a)}{}{C}_2 = \ ^{( a^2 - a)}{}{C}_4\] , then a =
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
Three persons enter a railway compartment. If there are 5 seats vacant, in how many ways can they take these seats?
The number of diagonals that can be drawn by joining the vertices of an octagon is
Among 14 players, 5 are bowlers. In how many ways a team of 11 may be formed with at least 4 bowlers?
Find n if `""^6"P"_2 = "n" ""^6"C"_2`
Find n and r if `""^"n""P"_"r"` = 720 and `""^"n""C"_("n" - "r")` = 120
Four parallel lines intersect another set of five parallel lines. Find the number of distinct parallelograms that can be formed.
Find the value of 15C4
Find the value of 80C2
A student has to answer 10 questions, choosing atleast 4 from each of Parts A and B. If there are 6 questions in Part A and 7 in Part B, in how many ways can the student choose 10 questions?
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 ______.
A box contains two white, three black and four red balls. In how many ways can three balls be drawn from the box, if atleast one black ball is to be included in the draw
A convex polygon has 44 diagonals. Find the number of its sides.
If nC12 = nC8, then n is equal to ______.
The number of ways in which we can choose a committee from four men and six women so that the committee includes at least two men and exactly twice as many women as men 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 total number of ways in which six ‘+’ and four ‘–’ signs can be arranged in a line such that no two signs ‘–’ occur together 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 ______.
A badminton club has 10 couples as members. They meet to organise a mixed double match. If each wife refers to p artner as well as oppose her husband in the match, then the number of different ways can the match off will be ______.
Total number of 6-digit numbers in which only and all the five digits 1, 3, 5, 7 and 9 appear is ______.
