Advertisements
Advertisements
प्रश्न
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 ______.
पर्याय
`""^((m + n + k))"C"_3`
`""^((m + n + k))"C"_3 - ""^n"C"_3 - ""^6"C"_3 - ""^k"C"_3`
mC3 + nC3 + kC3
mC3 × nC3 × kC3
उत्तर
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 `""^((m + n + k))"C"_3 - ""^n"C"_3 - ""^6"C"_3 - ""^k"C"_3`.
Explanation:
Here the total number of points are (m + n + k) which must give `""^((m + n + k))"C"_3` number of triangles but m points on l1 taking 3 points at a time gives mC3 combinations which produce no triangle.
Similarly, nC3 and kC3 number of triangles can not be formed.
Therefore, the required number of triangles is `""^((m + n + k))"C"_3 - ""^n"C"_3 - ""^6"C"_3 - ""^k"C"_3`.
APPEARS IN
संबंधित प्रश्न
In how many ways can a team of 3 boys and 3 girls be selected from 5 boys and 4 girls?
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.
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?
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:
L.C.M. (6!, 7!, 8!)
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 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 nC4 , nC5 and nC6 are in A.P., then 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 always selected;
From 4 officers and 8 jawans in how many ways can 6 be chosen (i) to include exactly one officer
Find the number of ways in which : (b) an arrangement, of four letters can be made from the letters of the word 'PROPORTION'.
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 + 1 = 20Cr − 1 , then r is equal to
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?
The number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines is
Find n and r if `""^"n""P"_"r"` = 720 and `""^"n""C"_("n" - "r")` = 120
Find the value of 15C4
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
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?
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 at least three girls.
There are 12 points in a plane of which 5 points are collinear, then the number of lines obtained by joining these points in pairs is 12C2 – 5C2.
If some or all of n objects are taken at a time, the number of combinations is 2n – 1.
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.
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 ______.
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 ______.
