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 ______.
विकल्प
`""^((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
Advertisements
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.
How many words, with or without meaning, each of 2 vowels and 3 consonants can be formed from the letters of the word DAUGHTER?
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?
Compute:
L.C.M. (6!, 7!, 8!)
In a class there are 27 boys and 14 girls. The teacher wants to select 1 boy and 1 girl to represent the class in a function. In how many ways can the teacher make this selection?
In how many ways can an examinee answer a set of ten true/false type questions?
Since the number has to be greater than 8000, the thousand's place can be filled by only two digits, i.e. 8 and 9.
Now, the hundred's place can be filled with the remaining 4 digits as the repetition of the digits is not allowed.
The ten's place can be filled with the remaining 3 digits.
The unit's place can be filled with the remaining 2 digits.
Total numbers that can be formed = `2xx4xx3xx2=48`
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?
Evaluate the following:
14C3
Evaluate the following:
12C10
If nC12 = nC5, find the value of n.
If n +2C8 : n − 2P4 = 57 : 16, find n.
If 2nC3 : nC2 = 44 : 3, find n.
A student has to answer 10 questions, choosing at least 4 from each of part A and part B. If there are 6 questions in part A and 7 in part B, in how many ways can the student choose 10 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 group consists of 4 girls and 7 boys. In how many ways can a team of 5 members be selected if the team has (ii) at least one boy and one girl?
In how many ways can a team of 3 boys and 3 girls be selected from 5 boys and 4 girls?
Out of 18 points in a plane, no three are in the same straight line except five points which are collinear. How many (i) straight lines
If 15C3r = 15Cr + 3 , then r is equal to
If C (n, 12) = C (n, 8), then C (22, n) is equal to
If\[\ ^{( a^2 - a)}{}{C}_2 = \ ^{( a^2 - a)}{}{C}_4\] , then a =
The number of ways in which a host lady can invite for a party of 8 out of 12 people of whom two do not want to attend the party together 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
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?
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?
A bag contains six white marbles and five red marbles. Find the number of ways in which four marbles can be drawn from the bag if two must be white and two red
A bag contains six white marbles and five red marbles. Find the number of ways in which four marbles can be drawn from the bag if they must all be of the same colour.
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 one boy and one girl
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 regular polygon has 20 sides. The number of triangles that can be drawn by using the vertices but not using the sides is
