Advertisements
Advertisements
प्रश्न
Find n if 2nC3 : nC2 = 52 : 3
Advertisements
उत्तर
2nC3 : nC2 = 52 : 3
∴ `(""^(2"n")"C"_3)/(""^"n""C"_2) = 52/3`
∴ `(2"n"!)/(3!(2"n" - 3)!) xx (2!("n" - 2)!)/("n"!) = 52/3`
∴ `(2"n"(2"n" - 1)(2"n" - 2)(2"n" - 3)!)/(3 xx 2 xx 1 xx (2"n" - 3)!) xx (2 xx 1 xx ("n" - 2)!)/("n"("n" - 1)("n" - 2)!) = 52/3`
∴ `(2 xx "n" xx (2"n" - 1)2("n" - 1))/(3 xx 2 xx 1) xx (2 xx 1)/("n"("n" - 1)) = 52/3`
∴ `(4(2"n" - 1))/3 = 52/3`
∴ 4(2n – 1) = 52
∴ 2n – 1 = `52/4`
∴ 2n – 1 = 13
∴ 2n = 14
∴ n = 7.
APPEARS IN
संबंधित प्रश्न
Find the value of 15C4
Find the value of `""^80"C"_2`
Find n if `""^"n""C"_("n" - 3)` = 84
If `""^"n""P"_"r" = 1814400` and `""^"n""C"_"r"` = 45, find r.
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 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 12 vowels are chosen?
Find n, if `""^"n""C"_("n" - 2)` = 15
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`
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?
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?
Find n if nCn–3 = 84
Find n and r if nPr = 720 and nCn–r = 120
Find n and r if nCr–1 : nCr : nCr+1 = 20 : 35 : 42
Find the number of ways of drawing 9 balls from a bag that has 6 red balls, 8 green balls, and 7 blue balls so that 3 balls of every colour are drawn
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.
Find the number of diagonals of an n-sided polygon. In particular, find the number of diagonals when n = 15
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 n if 21C6n = `""^21"C"_(("n"^2 + 5))`
Find n if 2nCr–1 = 2nCr+1
Find the differences between the greatest values in the following:
14Cr and 12Cr
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 majority?
A question paper has two sections. section I has 5 questions and section II has 6 questions. A student must answer at least two question 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?
Select the correct answer from the given alternatives.
A question paper has two parts, A and B, each containing 10 questions. If a student has to choose 8 from part A and 5 from part B, In how many ways can he choose the questions?
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
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:
Nine friends decide to go for a picnic in two groups. One group decides to go by car and the other group decides to go by train. Find the number of different ways of doing so if there must be at least 3 friends in each group.
Answer the following:
Find the number of ways of dividing 20 objects in three groups of sizes 8, 7 and 5
Answer the following:
Four parallel lines intersect another set of five parallel lines. Find the number of distinct parallelograms formed
If `1/(8!) + 1/(7!) = x/(9!)`, than x is equal to ______.
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 ______.
