JEE Mains · Maths · STD 11 - 6. permutation and combination
There are \(4\) men and \(5\) women in Group \(A\), and \(5\) men and \(4\) women in Group \(B.\) If \(4\) persons are selected from each group, then the number of ways of selecting \(4\) men and \(4\) women is ....................
- A \(9856\)
- B \(5626\)
- C \(4521\)
- D \(3574\)
Answer & Solution
Correct Answer
(B) \(5626\)
Step-by-step Solution
Detailed explanation
From Group \(A\) From Group \(B\) Ways of selection \(4M\) \(4W\) \({ }^4 \mathrm{C}_4{ }^4 \mathrm{C}_4=1\) \(3M\ \ 2W\) \(1M\ \ 3W\) \({ }^4 \mathrm{C}_3{ }^5 \mathrm{C}_1{ }^5 \mathrm{C}_1{ }^4 \mathrm{C}_3=400\) \(2M\ \ 2W\) \(2M\ \ 2W\)…
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
- Consider three boxes, each containing \(10\) balls labelled \(1, 2, ….., 10\). Suppose one ball is randomly drawn from each of the boxes. Denote by \(n_i\), the label of the ball drawn from the \(i^{th}\) box, \((i = 1, 2, 3)\). Then, the number of ways in which the balls can be chosen such that \(n_1 < n_2 < n_3\) is:JEE Mains 2019 Hard
- Let a focus of the ellipse \(E: \dfrac{x^2}{a^2} + \dfrac{y^2}{b^2} = 1\) be \(S(4, 0)\) and its eccentricity be \(\dfrac{4}{5}\). If the point \(P(3, \alpha)\) lies on \(E\) and \(O\) is the origin, then the area of \(\triangle POS\) is equal to:JEE Mains 2026 Medium
- \(\lim _{x \rightarrow \infty} \frac{\left(2 x^2-3 x+5\right)(3 x-1)^{\frac{x}{2}}}{\left(3 x^2+5 x+4\right) \sqrt{(3 x+2)^x}}\) is equal to :JEE Mains 2025 Medium
- Two vertical poles of heights, \(20\, m\) and \(80\,m\) stand a apart on a horizontal plane. The height (in meters) of the point of intersection of the lines joining the top of each pole to the foot of the other, from his horizontal plane isJEE Mains 2019 Hard
- Let the lines \(\frac{x-1}{\lambda}=\frac{y-2}{1}=\frac{z-3}{2}\) and \(\frac{ x +26}{-2}=\frac{ y +18}{3}=\frac{ z +28}{\lambda}\) be coplanar and \(P\) be the plane containing these two lines. Then which of the following points does \(NOT\) lies on \(P\)?JEE Mains 2022 Hard
- If the curve \(x^{2}+2 y^{2}=2\) intersects the line \(x + y =1\) at two points \(P\) and \(Q ,\) then the angle subtended by the line segment \(PQ\) at the origin is ...... .JEE Mains 2021 Medium
More PYQs from JEE Mains
- A group of \(40\) students appeared in an examination of \(3\) subjects - Mathematics, Physics Chemistry. It was found that all students passed in at least one of the subjects, \(20\) students passed in Mathematics, \(25\) students passed in Physics, \(16\) students passed in Chemistry, at most \(11\) students passed in both Mathematics and Physics, at most \(15\) students passed in both Physics and Chemistry, at most \(15\) students passed in both Mathematics and Chemistry. The maximum number of students passed in all the three subjects is ........... .JEE Mains 2024 Hard
- If a tangent to the ellipse \(x^{2}+4 y^{2}=4\) meets the tangents at the extremities of its major axis at \(\mathrm{B}\) and \(\mathrm{C}\), then the circle with \(\mathrm{BC}\) as diameter passes through the point:JEE Mains 2021 Hard
- An organization awarded \(48\) medals in event '\(A\)',\(25\) in event '\(B\) ' and \(18\) in event ' \(C\) '. If these medals went to total \(60\) men and only five men got medals in all the three events, then, how many received medals in exactly two of three events?JEE Mains 2023 Hard
- Let \(R\) be the focus of the parabola \(y^2=20 x\) and the line \(y=m x+c\) intersect the parabola at two points \(P\) and \(Q\). Let the point \(G(10,10)\) be the centroid of the triangle \(P Q R\). If \(c-m=6\), then \(( PQ )^2\) isJEE Mains 2023 Hard
- The number of 4-letter words, with or without meaning, which can be formed using the letters of 'PQRPQRSTUVP', is:JEE Mains 2026 Hard
- 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 toJEE Mains 2022 Hard