Advertisements
Advertisements
प्रश्न
Find n, if `""^(2"n")"C"_("r" - 1) = ""^(2"n")"C"_("r" + 1)`
उत्तर
`""^(2"n")"C"_("r" - 1) = ""^(2"n")"C"_("r" + 1)`
If nCx = nCy, then either x = y or x = n − y
∴ r −1 = r + 1 or r − 1 = 2n − (r + 1)
But r − 1 = r + 1 is not possible
∴ r − 1 = 2n − (r + 1)
∴ r + r = 2n
∴ n = r
APPEARS IN
संबंधित प्रश्न
Find the value of `""^80"C"_2`
Find the number of ways of selecting a team of 3 boys and 2 girls from 6 boys and 4 girls.
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 x if `""^"n""P"_"r" = "x" ""^"n""C"_"r"`
Find the differences between the largest values in the following: `""^13"C"_r "and" ""^8"C"_r`
Find n and r if nCr–1 : nCr : nCr+1 = 20 : 35 : 42
If nPr = 1814400 and nCr = 45, find n+4Cr+3
Find the number of diagonals of an n-sided polygon. In particular, find the number of diagonals when n = 15
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 four points are collinear
Find n if 21C6n = `""^21"C"_(("n"^2 + 5))`
Find n if 2nCr–1 = 2nCr+1
Find n if nCn–2 = 15
Find the value of `sum_("r" = 1)^4 ""^((21 - "r"))"C"_4`
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?
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?
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)]
