Advertisements
Advertisements
Question
Find r if 14C2r : 10C2r–4 = 143 : 10
Advertisements
Solution
14C2r : 10C2r–4 = 143 : 10
∴ `(14!)/(2"r"!(14 - 2"r")!) xx ((2"r" - 4)!(10 - 2"r" + 4)!)/(10!) = 143/10`
∴ `(14 xx 13 xx 12 xx 11 xx 10!)/(2"r"(2"r" - 1)(2"r" - 2)(2"r" - 3)(2"r" - 4)! xx (14 - 2"r")!) xx ((2"r" - 4)! xx (14 - 2"r")!)/(10!) = 143/10`
∴ `(14 xx 13 xx 12 xx 11)/(2"r"(2"r" - 1)(2"r" - 2)(2"r" - 3)) = 143/10`
∴ `(14 xx 12 xx 143)/(2"r"(2"r" - 1)(2"r" - 2)(2"r" - 3)) = 143/10`
∴ 14 × 12 × 10 = 2r(2r – 1)(2r – 2)(2r – 3)
∴ 2r(2r – 1)(2r – 2)(2r – 3) = 1680
∴ 2r(2r – 1)(2r – 2)(2r – 3) = 8 × 7 × 6 × 5
∴ 2r(2r – 1)(2r – 2)(2r – 3) = 8(8 – 1)(8 – 2)(8 – 3)
∴ 2r = 8 (by observation)
∴ r = 4.
APPEARS IN
RELATED QUESTIONS
Find the value of 15C4
Find the value of `""^20"C"_16 - ""^19"C"_16`
Find n if `""^"n""C"_("n" - 3)` = 84
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-shaded polygon. In particular, find the number of diagonals when: n = 10
Ten points are plotted on a plane. Find the number of straight lines obtained by joining these points if no three points are collinear.
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 the number of triangles formed by joining 12 points if four points are collinear.
Find n if `""^"n""C"_8 = ""^"n""C"_12`
Find n, if `""^21"C"_(6"n") = ""^21"C"_(("n"^2 + 5)`
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
If nPr = 1814400 and nCr = 45, find n+4Cr+3
If nCr–1 = 6435, nCr = 5005, nCr+1 = 3003, find rC5
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
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 value of `sum_("r" = 1)^4 ""^((21 - "r"))"C"_4`
Find the differences between the greatest values in the following:
14Cr and 12Cr
Find the differences between the greatest values in the following:
15Cr and 11Cr
In how many ways can a boy invite his 5 friends to a party so that at least three join the party?
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?
Five students are selected from 11. How many ways can these students be selected if two specified students are selected?
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.
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
The maximum value of z = 9x + 11y subject to 3x + 2y ≤ 12, 2x + 3y ≤ 12, x ≥ 0, y ≥ 0 is _______.
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 ______.
