JEE Mains · Maths · STD 11 - 6. permutation and combination
There are ten boys \(B_{1}, B_{2}, \ldots ., B_{10}\) and five girls \(G_{1}\), \(G _{2}, \ldots, G _{5}\) in a class. Then the number of ways of forming a group consisting of three boys and three girls, if both \(B_{1}\) and \(B_{2}\) together should not be the members of a group, is
- A \(1119\)
- B \(1120\)
- C \(1121\)
- D \(1122\)
Answer & Solution
Correct Answer
(B) \(1120\)
Step-by-step Solution
Detailed explanation
\(n ( B )=10\) \(n ( a )=5\) The number of ways of forming a group of \(3\) girls of \(3\) boys. \(={ }^{10} C _{3} \times{ }^{5} C _{3}\) \(=\frac{10 \times 9 \times 8}{3 \times 2} \times \frac{5 \times 4}{2}=1200\) The number of ways when two particular boys \(B_{1}\) of…
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
- If \(\lim _{x \rightarrow 0} \frac{e^{a x}-\cos (b x)-\frac{c x e^{-c x}}{2}}{1-\cos (2 x)}=17\), then \(5 a ^2+ b ^2\) is equal toJEE Mains 2023 Hard
- If all the words with or without meaning made using all the letters of the word "NAGPUR" are arranged as in a dictionary, then the word at \(315^{\text {th }}\) position in this arrangement is :JEE Mains 2024 Medium
- The mean of a set of \(30\) observations is \(75\). If each other observation is multiplied by a nonzero number \(\lambda \) and then each of them is decreased by \(25\), their mean remains the same. The \(\lambda \) is equal toJEE Mains 2018 Hard
- Let \(S\) be the set of all values of \(\theta \in[-\pi, \pi]\) for which the system of linear equations \(x+y+\sqrt{3} z=0\) \(-x+(\tan \theta) y+\sqrt{7} z=0\) \(x+y+(\tan \theta) z=0\) has non-trivial solution. Then \(\frac{120}{\pi} \sum_{\theta \in s} \theta\) is equal toJEE Mains 2023 Hard
- If the differential equation representing the family of all circles touching \(x-\) axis at the origin is \(\left( {{x^2} - {y^2}} \right)\frac{{dy}}{{dx}} = g\left( x \right)y\) , then \(g(x)\) equalsJEE Mains 2014 Hard
- Let \(z\) and \(w\) be two complex numbers such that \(w=z \bar{z}-2 z+2,\left|\frac{z+i}{z-3 i}\right|=1\) and \(\operatorname{Re}(w)\) has minimum value. Then, the minimum value of \(n \in N\) for which \(w ^{ n }\) is real, is equal to..........JEE Mains 2021 Hard
More PYQs from JEE Mains
- Let the sum of the first three terms of an \(A. P,\) be \(39\) and the sum of its last four terms be \(178.\) If the first term of this \(A.P.\) is \(10,\) then the median of the \(A.P.\) isJEE Mains 2015 Hard
- If \(A = \left[ {\begin{array}{*{20}{c}}
1&{\sin \,\theta }&1\\
{ - \,\sin \,\theta }&1&{\sin \,\theta }\\
{ - 1}&{ - \,\sin \,\theta }&1
\end{array}} \right];\) then for all \(\theta \, \in \,\left( {\frac{{3\pi }}{4},\frac{{5\pi }}{4}} \right),\) det \((A)\) lies in the intervalJEE Mains 2019 Hard - Let \(a, b, c, d\) and \(p\) be any non zero distinct real numbers such that \(\left(a^{2}+b^{2}+c^{2}\right) p^{2}-2(a b+b c+ cd ) p +\left( b ^{2}+ c ^{2}+ d ^{2}\right)=0 .\) ThenJEE Mains 2020 Hard
- Let \(S_{1}: x^{2}+y^{2}=9\) and \(S_{2}:(x-2)^{2}+y^{2}=1\). Then the locus of center of a variable circle \(S\) which touches \(S_{1}\) internally and \(S_{2}\) externally always passes through the points :JEE Mains 2021 Hard
- The sum of the first three terms of a \(G.P.\) is \(S\) and their product is \(27 .\) Then all such \(S\) lie inJEE Mains 2020 Medium
- The shortest distance between lines \(\mathrm{L}_1\) and \(\mathrm{L}_2\), where \(L_1: \frac{x-1}{2}=\frac{y+1}{-3}=\frac{z+4}{2}\) and \(L_2\) is the line passing through the points \(\mathrm{A}(-4,4,3) \cdot \mathrm{B}(-1,6,3)\) and perpendicular to the line \(\frac{x-3}{-2}=\frac{y}{3}=\frac{z-1}{1}\), isJEE Mains 2024 Hard