Advertisements
Advertisements
प्रश्न
Answer the following:
Four parallel lines intersect another set of five parallel lines. Find the number of distinct parallelograms formed
Advertisements
उत्तर
To form a parallelogram, we have to select any 2 of 4 parallel lines and any 2 of another 5 parallel lines for intersecting.
∴ the number of parallelograms which can be formed
= 4C2 × 5C2
= `(4!)/(2!2!) xx (5!)/(2!3!)`
= `(4 xx 3)/(2 xx 1) xx (5 xx 4)/(2 xx 1)`
= 6 × 10
= 60.
APPEARS IN
संबंधित प्रश्न
Find the value of 15C4
Find the value of `""^80"C"_2`
Find the value of `""^20"C"_16 - ""^19"C"_16`
Find r if `""^14"C"_(2"r"): ""^10"C"_(2"r" - 4)` = 143:10
If 20 points are marked on a circle, how many chords can be drawn?
Find the number of diagonals of an n-shaded polygon. In particular, find the number of diagonals when: n = 10
Find the number of diagonals of an n-shaded polygon. In particular, find the number of diagonals when: n = 12
Ten points are plotted on a plane. Find the number of straight lines obtained by joining these points if four points are collinear.
Find the number of triangles formed by joining 12 points if no three points are collinear,
Find n, if `""^"n""C"_("n" - 2)` = 15
find the value of `sum_("r" = 1)^4 ""^(21 - "r")"C"_4 + ""^17"C"_5`
A group consists of 9 men and 6 women. A team of 6 is to be selected. How many of possible selections will have at least 3 women?
A committee of 10 persons is to be formed from a group of 10 women and 8 men. How many possible committees will have at least 5 women? How many possible committees will have men in the majority?
Find n and r if nPr = 720 and nCn–r = 120
After a meeting, every participant shakes hands with every other participants. If the number of handshakes is 66, find the number of participants in the meeting.
If 20 points are marked on a circle, how many chords can be drawn?
Find the number of diagonals of an n-sided polygon. In particular, find the number of diagonals when n = 12
Find the number of diagonals of an n-sided polygon. In particular, find the number of diagonals when n = 8
There are 20 straight lines in a plane so that no two lines are parallel and no three lines are concurrent. Determine the number of points of intersection
Ten points are plotted on a plane. Find the number of straight lines obtained by joining these points if no three points are collinear
Find the number of triangles formed by joining 12 points if four points are collinear
A word has 8 consonants and 3 vowels. How many distinct words can be formed if 4 consonants and 2 vowels are chosen?
Find n if nC8 = nC12
Find n if nCn–2 = 15
Find the value of `sum_("r" = 1)^4 ""^((21 - "r"))"C"_4`
Find the differences between the greatest values in the following:
14Cr and 12Cr
Five students are selected from 11. How many ways can these students be selected if two specified students are selected?
Select the correct answer from the given alternatives.
The number of arrangements of the letters of the word BANANA in which two N's do not appear adjacently
Answer the following:
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
Answer the following:
A student finds 7 books of his interest but can borrow only three books. He wants to borrow the Chemistry part-II book only if Chemistry Part-I can also be borrowed. Find the number of ways he can choose three books that he wants to borrow.
Answer the following:
Find the number of ways of dividing 20 objects in three groups of sizes 8, 7 and 5
The maximum value of z = 9x + 11y subject to 3x + 2y ≤ 12, 2x + 3y ≤ 12, x ≥ 0, y ≥ 0 is _______.
In how many ways can a group of 5 boys and 6 girls be formed out of 10 boys and 11 girls?
Out of 7 consonants and 4 vowels, the number of words (not necessarily meaningful) that can be made, each consisting of 3 consonants and 2 vowels, is ______.
