MHT CET · Maths · Permutation Combination
Five students are selected from n students such that the ratio of number of ways in which 2 particular students are selected to the number of ways 2 particular students not selected is \(2: 3\). Then the value of \(\mathrm{n}\) is
- A 5
- B 6
- C 11
- D not possible
Answer & Solution
Correct Answer
(C) 11
Step-by-step Solution
Detailed explanation
Five students are selected from \(\mathrm{n}\) students. Number of ways in which 2 particular students are sélected \(=\mathrm{n}^{-2} \mathrm{C}_3\)
Number of ways in which 2 particular students are not selected \(={ }^{\mathrm{n}-2} \mathrm{C}_5\)
\(\therefore\) According to the given condition,
\(\frac{{ }^{n-2} C_3}{{ }^{n-2} C_5}=\frac{2}{3}\)
\(\begin{aligned} & \Rightarrow \frac{(\mathrm{n}-2) !}{3 !(\mathrm{n}-5) !} \times \frac{5 !(\mathrm{n}-7) !}{(\mathrm{n}-2) !}=\frac{2}{3} \\ & \Rightarrow(\mathrm{n}-5)(\mathrm{n}-6)=30 \\ & \Rightarrow \mathrm{n}=11\end{aligned}\)
Number of ways in which 2 particular students are not selected \(={ }^{\mathrm{n}-2} \mathrm{C}_5\)
\(\therefore\) According to the given condition,
\(\frac{{ }^{n-2} C_3}{{ }^{n-2} C_5}=\frac{2}{3}\)
\(\begin{aligned} & \Rightarrow \frac{(\mathrm{n}-2) !}{3 !(\mathrm{n}-5) !} \times \frac{5 !(\mathrm{n}-7) !}{(\mathrm{n}-2) !}=\frac{2}{3} \\ & \Rightarrow(\mathrm{n}-5)(\mathrm{n}-6)=30 \\ & \Rightarrow \mathrm{n}=11\end{aligned}\)
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
- The area bounded by the parabola \(\mathrm{y}^2=4 \mathrm{ax}\) and its latus-rectum \(x=a\) isMHT CET 2021 Medium
- The line \(\frac{x-2}{3}=\frac{y-1}{-5}=\frac{z+2}{2}\) lies in the plane \(x+3 y-\alpha z+\beta=0\), then the value of \(\alpha^2+\alpha \beta+\beta^2\) isMHT CET 2023 Medium
- The curve \(x^4-2 x y^2+y^2+3 x-3 y=0\) cuts the X -axis at \((0,0)\) at an angle ofMHT CET 2024 Hard
- \(\int \frac{\sin 2 x}{\sin ^{2} x \cos ^{2} x} d x=\)MHT CET 2020 Medium
- Let two cards are drawn at random from a pack of 52 playing cards. Let \(\mathrm{X}\) be the number of aces obtained. Then the values of \(\mathrm{E}(\mathrm{X})\) isMHT CET 2021 Medium
- If \(\bar{a}=2 \hat{i}-\hat{j}+\hat{k}, \bar{b}=\hat{i}+2 \hat{j}-3 \hat{k}\) and \(\bar{c}=3 \hat{i}+\lambda \hat{j}+5 \hat{k}\) are coplanar, then \(\lambda\) is the root of the equationMHT CET 2021 Easy
More PYQs from MHT CET
- Three bodies P, Q and R have masses ' \(\mathrm{m}\) ' \(\mathrm{kg}\), ' \(2 \mathrm{~m}\) ' \(\mathrm{kg}\) and ' \(3 \mathrm{~m}\) ' \(\mathrm{kg}\) respectively. If all the bodies have equal kinetic energy, then greater momentum will be for body/bodies.MHT CET 2021 Easy
- Identify ' \(\mathrm{B}^{\prime}\) in the following series of reactions
\(
\text {Ethanol } \frac{\mathrm{NaBr}}{\mathrm{H}_{2} \mathrm{SO}_{4}, \Delta} \quad \mathrm{A} \quad \frac{\mathrm{Mg}}{\text { Dry ether }}{\longrightarrow} \mathrm{B}
\)MHT CET 2020 Hard - \(\int_{\frac{\pi}{4}}^{\frac{3 \pi}{4}} \frac{d x}{1+\cos x}\) is equal toMHT CET 2022 Easy
- With usual notations in \(\Delta \mathrm{ABC}, \mathrm{a}=3, \mathrm{c}=2\) and \(\sin \mathrm{C}=\frac{2}{3}\), then \(\angle \mathrm{A}=\)MHT CET 2020 Easy
- If \((\mathrm{a}+\mathrm{b}) \cos \mathrm{C}+(\mathrm{b}+\mathrm{c}) \cos \mathrm{A}+(\mathrm{c}+\mathrm{a}) \cos \mathrm{B}=72\) and if \(\mathrm{a}=18, \mathrm{~b}=24\), then area of the triangle ABC isMHT CET 2024 Hard
- Which one of the following is INCORRECT about population interaction?MHT CET 2023 Hard