JEE Mains · Maths · STD 11 - 6. permutation and combination
The number of ways to distribute \(30\) identical candies among four children \(C _{1}, C _{2}, C _{3}\) and \(C _{4}\) so that \(C _{2}\) receives atleast \(4\) and atmost \(7\) candies, \(C _{3}\) receives atleast \(2\)and atmost \(6\) candies, is equal to
- A \(205\)
- B \(615\)
- C \(510\)
- D \(430\)
Answer & Solution
Correct Answer
(D) \(430\)
Step-by-step Solution
Detailed explanation
\(t_{1}+t_{2}+t_{3}+t_{4}=30\) Coefficient of \(x^{30}\) in \(\left(1+x+x^{2}+\ldots+x^{30}\right)^{2}\) \(\left(x^{4}+x^{5}+x^{6}+x^{7}\right)\left(x^{2}+x^{3}+x^{4}+x^{5}+x^{6}\right)\)…
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- Let \(y=y(x)\) be the solution of the differential equation \(x \log _e x \frac{d y}{d x}+y=x^2 \log _e x,(x > 1)\). If \(y (2)=2\), then \(y ( e )\) is equal toJEE Mains 2023 Hard
- If the curve, \(y = y ( x )\) represented by the solution of the differential equation \(\left(2 x y^{2}-y\right) d x+x d y=0,\) passes through the intersection of the lines, \(2 x -3 y =1\) and \(3 x+2 y=8,\) then \(|y(1)|\) is equal to ...... .JEE Mains 2021 Hard
- Statement \(1\) : The only circle having radius \(\sqrt {10} \) and a diameter along line \(2x + y = 5\) is \(x^2 + y^2 - 6x +2y = 0\).
Statement \(2\) : \(2x + y = 5\) is a normal to the circle \(x^2 + y^2 -6x+2y = 0\).JEE Mains 2013 Hard - Let the plane \(ax \,\,+\,\,by \,\,+c z=d\) pass through \((2,3,-5)\) and is perpendicular to the planes \(2 x + y -5 z =10\) and \(3 x+5 y-7 z=12\). If \(a, b, c, d\) are integers \(d>0\) and gcd \((lal, |b|,|c|, d)\) \(=1\), then the value of \(a+7 b+c+20 \,d\) is equal toJEE Mains 2022 Hard
- Let the equation \(x^{2}+y^{2}+p x+(1-p) y+5=0\) represent circles of varying radius \(\mathrm{r} \in(0,5]\). Then the number of elements in the set \(S=\left\{q: q=p^{2}\right.\) and \(\mathrm{q}\) is an integer \(\}\) is ..... .JEE Mains 2021 Hard
- Let \(f(x)=x^{2025}-x^{2000}, x\in[0,1]\)and the minimum value of the function \(f(x)\) in the interval [0, 1] be \((80)^{80}(n)^{-81}\). Then n is equal toJEE Mains 2026 Hard
More PYQs from JEE Mains
- Let \(A=\{(x, y): 2 x+3 y=23, x, y \in N\}\) and \(B=\{x:(x, y) \in A\}\). Then the number of one-one functions from \(\mathrm{A}\) to \(\mathrm{B}\) is equal to ................JEE Mains 2024 Medium
- In a \(\Delta ABC,\frac{a}{b} = 2 + \sqrt 3 \) and \(\angle C\, = \,{60^o}.\) Then the ordered pair \((\angle A,\angle B)\) is equal toJEE Mains 2015 Hard
- The coefficient of \(x^{4}\) in the expansion of \(\left(1+x+x^{2}+x^{3}\right)^{6}\) in powers of \(x,\) isJEE Mains 2020 Medium
- \(f(x)=\left\{\begin{array}{cc}\frac{\sin (x-[x])}{x-[x]} & , \quad x \in(-2,-1) \\ \max \{2 x, 3[|x|]\} & , \quad|x|<1 \\ 1 & , \quad \text { otherwise }\end{array}\right.\) where \([t]\) denotes greatest integer \(\leq t\). If \(m\) is the number of points where \(f\) is not continuous and \(n\) is the number of points where \(f\) is not differentiable, then the ordered pair \(( m , n )\) isJEE Mains 2022 Hard
- If the ratio of the fifth term from the begining to the fifth term from the end in the expansion of \(\left(\sqrt[4]{2}+\frac{1}{\sqrt[4]{3}}\right)^n\) is \(\sqrt{6}: 1\), then the third term from the beginning is:JEE Mains 2023 Hard
- Let \(\mathrm{x}=\frac{\mathrm{m}}{\mathrm{n}}\) ( \(\mathrm{m}, \mathrm{n}\) are co-prime natural numbers) be a solution of the equation \(\cos \left(2 \sin ^{-1} x\right)=\frac{1}{9}\) and let \(\alpha, \beta(\alpha>\beta)\) be the roots of the equation \(\mathrm{mx}^2-\mathrm{nx}-\) \(\mathrm{m}+\mathrm{n}=0\). Then the point \((\alpha, \beta)\) lies on the lineJEE Mains 2024 Medium