AP EAMCET · Maths · Permutation Combination
If 3 sisters and 8 brothers are together playing a game, then the number of ways in which all the sisters and brothers are to be seated around a circle such that all the three sisters are not seated together is
- A \(8!\times 504\)
- B \(11!\times 8\)
- C \(7!\times 210\)
- D \(8!\times 84\)
Answer & Solution
Correct Answer
(D) \(8!\times 84\)
Step-by-step Solution
Detailed explanation
Total arrangements: \((11-1)! = 10!\) Arrangements where 3 sisters are together: \((8+1-1)! \times 3! = 8! \times 3!\) Arrangements where sisters are not together: \(10! - (8! \times 3!) = 10 \times 9 \times 8! - 6 \times 8! = 8!(90 - 6) = 8! \times 84\)
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 the angle between the circles \(x^2+y^2-2 x-4 y+c=0\) and \(x^2+y^2-4 x-2 y+4=0\) is \(60^{\circ}\), then \(c\) is equal toAP EAMCET 2016 Medium
- Ifsin \(\left(x+\frac{\pi}{3}\right)+\sin \left(x-\frac{\pi}{3}\right)=1\), then the value of \(x\) in the interval \([0, \pi]\)AP EAMCET 2022 Easy
- The number of ways of awarding 9 scholarships among three students so that each may have 3 scholarships isAP EAMCET 2017 Medium
- The coefficient of \(x^3 y^4 z^5\) in the expansion of \((x y+y z+x z)^6\) isAP EAMCET 2005 Medium
- If \(\cos ^{-1}\left(\frac{x^2-y^2}{x^2+y^2}\right)=\sin ^{-1}(a)\) then \(\frac{d y}{d x}\) is equal toAP EAMCET 2020 Easy
- For a binomial variate \(X \sim B(n, p)\) the difference between the mean and variance is 1 and the difference between their squares is 11 . If the probability of \(P(x=2)=m\left(\frac{5}{6}\right)^n\) and \(n=36\) then \(m: n=\)AP EAMCET 2024 Hard
More PYQs from AP EAMCET
- If the number of diagonals of a regular polygon is 35, then the number of sides of the polygon isAP EAMCET 2025 Medium
- Which among the following possesses a \(s p\) carbon in its structure?AP EAMCET 2021 Easy
- Which one of the statements, regarding X is not correct ?
3-Hydroxybutanoic acid + 3-Hydroxypentanoic acid \(\longrightarrow \mathrm{X}\)AP EAMCET 2025 Medium - Let \(D\) be the domain of a twice differentiable function \(f\). For all \(x \in D, f^{\prime \prime}(x)+f(x)=0\) and \(f(x)=\int g(x) d x+\) constant. If \(h(x)=\{\mathrm{f}(x)\}^2+\{g(x)\}^2\) and \(h(0)=5\), then \(h(2015)-h(2014)\) is equal toAP EAMCET 2015 Hard
- The solution of \(\frac{d^2 y}{d x^2}=0\) representsAP EAMCET 2020 Easy
- If \(u(x, y)=y \log x+x \log y\), then \(u_x u_y-u_x \log x-u_y \log y+\log x \log y\) is equal to :AP EAMCET 2003 Hard