Advertisements
Advertisements
Question
Find r if `""^14"C"_(2"r"): ""^10"C"_(2"r" - 4)` = 143:10
Solution
`""^14"C"_(2"r"): ""^10"C"_(2"r" - 4)` = 143:10
`∴(14!)/(2"r"!(14-2"r")!)÷(10!)/((2"r" - 4)!(14-2"r")!) = 143/10`
∴ `(14!)/(2"r"!(14 - 2"r")!) xx ((2"r" - 4)!(14-2"r")!)/(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)!(14-2"r")!)xx((2"r"-4)!(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`
∴ 2r(2r – 1) . (2r – 2) (2r – 3) = 14 × 12 × 10
∴ 2r(2r – 1) . (2r – 2) (2r – 3) = 8 × 7 × 6 × 5
Comparing on both sides, we get
∴ r = 4
APPEARS IN
RELATED QUESTIONS
Find the value of `""^80"C"_2`
Find n and r if `""^"n""C"_("r" - 1): ""^"n""C"_"r": ""^"n""C"_("r" + 1)` = 20:35:42
Find n, if `""^(2"n")"C"_("r" - 1) = ""^(2"n")"C"_("r" + 1)`
Find r if `""^11"C"_4 + ""^11"C"_5 + ""^12"C"_6 + ""^13"C"_7 = ""^14"C"_"r"`
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 and r if nCr–1 : nCr : nCr+1 = 20 : 35 : 42
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 = 8
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 23C3n = 23C2n+3
Find n if nCn–2 = 15
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?
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
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 ______.
