Advertisements
Advertisements
प्रश्न
Find the number of triangles formed by joining 12 points if no three points are collinear
उत्तर
A triangle can be formed by selecting 3 non-collinear points.
We can choose 3 points from 12 points in
12C3 = `(12!)/(3!9!)`
= `(12 xx 11 xx 10 xx 9!)/(3 xx 2 xx 1 xx 9!)`
= 220 ways
∴ number of triangles = 220.
APPEARS IN
संबंधित प्रश्न
Find the value of 15C4
Find the value of `""^15"C"_4 + ""^15"C"_5`
Find n if `""^"n""C"_("n" - 3)` = 84
Find r if `""^14"C"_(2"r"): ""^10"C"_(2"r" - 4)` = 143:10
Find n and r if `""^"n""C"_("r" - 1): ""^"n""C"_"r": ""^"n""C"_("r" + 1)` = 20:35:42
Find the number of diagonals of an n-shaded polygon. In particular, find the number of diagonals when: n = 12
Find n, if `""^(2"n")"C"_("r" - 1) = ""^(2"n")"C"_("r" + 1)`
find the value of `sum_("r" = 1)^4 ""^(21 - "r")"C"_4 + ""^17"C"_5`
Find the differences between the largest values in the following: `""^14"C"_r "and" ""^12"C"_r`
Find the differences between the largest values in the following: `""^13"C"_r "and" ""^8"C"_r`
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 question paper has two sections. section I has 5 questions and section II has 6 questions. A student must answer at least two questions from each section among 6 questions he answers. How many different choices does the student have in choosing questions?
Five students are selected from 11. How many ways can these students be selected if two specified students are selected?
Find n if 2nC3 : nC2 = 52 : 3
Find n and r if nCr–1 : nCr : nCr+1 = 20 : 35 : 42
Find the number of ways of selecting a team of 3 boys and 2 girls from 6 boys and 4 girls
Find the number of diagonals of an n-sided polygon. In particular, find the number of diagonals when n = 10
Find the number of diagonals of an n-sided polygon. In particular, find the number of diagonals when n = 12
Find n if 2nCr–1 = 2nCr+1
Find n if nCn–2 = 15
Find r if 11C4 + 11C5 + 12C6 + 13C7 = 14Cr
Find the differences between the greatest values in the following:
14Cr and 12Cr
Find the differences between the greatest values in the following:
13Cr and 8Cr
There are 3 wicketkeepers and 5 bowlers among 22 cricket players. A team of 11 players is to be selected so that there is exactly one wicketkeeper and at least 4 bowlers in the team. How many different teams can be formed?
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
Select the correct answer from the given alternatives.
The number of ways in which 5 male and 2 female members of a committee can be seated around a round table so that the two females are not seated together is
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:
30 objects are to be divided in three groups containing 7, 10, 13 objects. Find the number of distinct ways for doing so.
A student passes an examination if he secures a minimum in each of the 7 subjects. Find the number of ways a student can fail.
Answer the following:
Find the number of ways of dividing 20 objects in three groups of sizes 8, 7 and 5
If `1/(8!) + 1/(7!) = x/(9!)`, than x is equal to ______.
If vertices of a parallelogram are respectively (2, 2), (3, 2), (4, 4), and (3, 4), then the angle between diagonals is ______
What is the probability of getting a “FULL HOUSE” in five cards drawn in a poker game from a standard pack of 52-cards?
[A FULL HOUSE consists of 3 cards of the same kind (eg, 3 Kings) and 2 cards of another kind (eg, 2 Aces)]
