JEE Mains · Maths · STD 11 - 14. probability
If \(10\) different balls are to be placed in \(4\) distinct boxes at random, then the probability that two of these boxes contain exactly \(2\) and \(3\) balls is
- A \(\frac{945}{2^{11}}\)
- B \(\frac{965}{2^{11}}\)
- C \(\frac{945}{2^{10}}\)
- D \(\frac{965}{2^{10}}\)
Answer & Solution
Correct Answer
(C) \(\frac{945}{2^{10}}\)
Step-by-step Solution
Detailed explanation
Total ways \(=4^{10}=\mathrm{n}\) Number of ways placing exactly 2 and 3 balls in two of these boxes \(=^{4} \mathrm{C}_{2} \times \frac{ 5!}{ 2! {3!}} \times 2! \times^{10} \mathrm{C}_{5} \times 2^{5}=\mathrm{m}\) Required probability…
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 the tangent to the circle \(C _{1}: x^{2}+y^{2}=2\) at the point \(M (-1,1)\) intersect the circle \(C _{2}\) : \(( x -3)^{2}+(y-2)^{2}=5\), at two distinct points \(A\) and \(B\). If the tangents to \(C _{2}\) at the points \(A\) and \(B\) intersect at \(N\), then the area of the triangle \(ANB\) is equal toJEE Mains 2022 Hard
- Let a line \(L_1\) pass through the origin and be perpendicular to the lines
\(L_2: \vec{r} = (3+t)\hat{i} + (2t-1)\hat{j} + (2t+4)\hat{k}\) and
\(L_3: \vec{r} = (3+2s)\hat{i} + (3+2s)\hat{j} + (2+s)\hat{k}\), \(t, s \in \mathbb{R}\).
If \((a, b, c)\), \(a \in \mathbb{Z}\), is the point on \(L_3\) at a distance of \(\sqrt{17}\) from the point of intersection of \(L_1\) and \(L_2\), then \((a+b+c)^2\) is equal to ________.JEE Mains 2026 Hard - If a circle \(C\) passing through \((4, 0)\) touches the circle \(x^2 + y^2 + 4x - 6y - 12 = 0\) externally at a point \((1, -1),\) then the radius of the circle \(C\) isJEE Mains 2013 Hard
- Let \(y = y _1( x )\) and \(y = y _2( x )\) be the solution curves of the differential equation \(\frac{d y}{d x}=y+7\) with initial conditions \(y_1(0)=0, y_2(0)=1\) respectively. Then the curves \(y=y_1(x)\) and \(y=y_2(x)\) intersect atJEE Mains 2023 Hard
- The coefficient of \(x ^7\) in \(\left(1-x+2 x^3\right)^{10}\) is \(........\).JEE Mains 2023 Hard
- Given three indentical bags each containing 10 balls, whose colours are as follows :
\(\begin{array}{cccc} & \text{Red} & \text{Blue} & \text{Green} \\ \text{Bag I} & 3 & 2 & 5 \\ \text{Bag II} & 4 & 3 & 3 \\ \text{Bag III} & 5 & 1 & 4\end{array}\)
A person chooses a bag at random and takes out a ball. If the ball is Red, the probability that it is from bag I is p and if the balls is Green, the probability that it is from bag III is q , then the value of \(\left(\frac{1}{\mathrm{p}}+\frac{1}{\mathrm{q}}\right)\) is :JEE Mains 2025 Easy
More PYQs from JEE Mains
- Let \(\overrightarrow{\mathrm{a}}=3 \hat{i}-\hat{j}+2 \hat{k}, \overrightarrow{\mathrm{~b}}=\overrightarrow{\mathrm{a}} \times(\hat{i}-2 \hat{k})\) and \(\overrightarrow{\mathrm{c}}=\overrightarrow{\mathrm{b}} \times \hat{k}\). Then the projection of \(\overrightarrow{\mathrm{c}}-2 \hat{j}\) on \(\vec{a}\) is :JEE Mains 2025 Medium
- A rod of length eight units moves such that its ends \(A\) and \(B\) always lie on the lines \(x-y+2=0\) and \(y+2=0\), respectively. If the locus of the point \(P\), that divides the rod \(A B\) internally in the ratio \(2: 1\) is \(9\left(x^2+\alpha y^2+\beta x y+\gamma x+28 y\right)-76=0\), then \(\alpha-\beta-\gamma\) is equal to :JEE Mains 2025 Hard
- \(\int \frac{\left(x^{2}+1\right) e^{x}}{(x+1)^{2}} d x=f(x) e^{x}+C\), Where \(C\) is a constant, then \(\frac{d^{3} f}{d x^{3}}\) at \(x =1\) is equal toJEE Mains 2022 Hard
- The value of the integral \(\displaystyle\int_0^\infty \dfrac{\log_e(x)}{x^2 + 4}\,dx\) is:JEE Mains 2026 Hard
- \(\begin{aligned}
& \text { If } \frac{1}{1^4}+\frac{1}{2^4}+\frac{1}{3^4}+\ldots . . \infty=\frac{\pi^4}{90}, \\
& \frac{1}{1^4}+\frac{1}{3^4}+\frac{1}{5^4}+\ldots . . \infty=\alpha, \\
& \frac{1}{2^4}+\frac{1}{4^4}+\frac{1}{6^4}+\ldots . \infty=\beta,
\end{aligned}\)
then \(\frac{\alpha}{\beta}\) is equal toJEE Mains 2025 Medium - If each of the lines \(5x + 8y = 13\) and \(4x - y = 3\) contains a diameter of the circle
\(x^2 + y^2 - 2\,(a^2 - 7a + 11)\) \(x - 2\, ( a^2 - 6a + 6)\, y + b^3 + 1 = 0\), thenJEE Mains 2013 Hard