MHT CET · Maths · Permutation Combination
Out of 7 consonants and 4 vowels, the number of words consisting of 3 consonants and 2 vowels are
- A 3300
- B 210
- C 120
- D 25200
Answer & Solution
Correct Answer
(D) 25200
Step-by-step Solution
Detailed explanation
We have to choose 3 consonants and 2 vowels from 7 consonants and 4 vowels.
\(\therefore\) Number of words \(=\left({ }^7 \mathrm{C}_3\right) \times\left({ }^4 \mathrm{C}_2\right) \times 5\) !
\(=\frac{7 !}{3 ! 4 !} \times \frac{4 !}{2 ! 2 !} \times 5 !=25200\)
\(\therefore\) Number of words \(=\left({ }^7 \mathrm{C}_3\right) \times\left({ }^4 \mathrm{C}_2\right) \times 5\) !
\(=\frac{7 !}{3 ! 4 !} \times \frac{4 !}{2 ! 2 !} \times 5 !=25200\)
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 \(A=\left[\begin{array}{ll}2 & 3 \\ 1 & 2\end{array}\right], B=\left[\begin{array}{ll}1 & 0 \\ 3 & 1\end{array}\right]\), then \((A B)^{-1}=\)MHT CET 2020 Easy
- The rate of change of the volume of a sphere with respect to its surface area, when its radius is 2 cm, is _______ \(\mathrm{cm}^3 / \mathrm{cm}^2\).MHT CET 2024 Easy
- The focal distance of a point \(P\) on the parabola \(y^{2}=12 x\) if the ordinate of \(P\) is 6, isMHT CET 2009 Easy
- In a triangle \(A B C\), with usual notation, \(\angle B=\pi / 3, \angle C=\pi / 4 . D\) divides \(B C\) internally in the ratio 1:3 then \(\frac{\sin \angle \mathrm{BAD}}{\sin \angle \mathrm{CAD}}\)MHT CET 2025 Medium
- AOB is the positive quadrant of the ellipse \(\frac{x^2}{25}+\frac{y^2}{9}=1\) in which \(\mathrm{OA}=5, \mathrm{OB}=3\). The area between the \(\operatorname{arc} \mathrm{AB}\) and the chord AB of the ellipse in sq.units isMHT CET 2025 Medium
- \(\int \frac{\sec x}{\sqrt{\log (\sec x+\tan x)}} d x=\)MHT CET 2020 Easy
More PYQs from MHT CET
- For all real \(x\), the minimum value of the function \(f(x)=\frac{1-x+x^2}{1+x+x^2}\) isMHT CET 2021 Medium
- If , then at isMHT CET 2018 Easy
- Which among the following compounds is used to decaffeinate coffee?MHT CET 2019 Easy
- In hydrogen atom in its ground state, the first Bohr orbit has radius ' \(r_1{ }^{\prime}\). When the atom is raised to one of its excited states, the electrons orbital velocity becomes one-third. The radius of that orbit isMHT CET 2025 Medium
- A dihaloalkane ' \(X\), having formula \(\mathrm{C}_{3} \mathrm{H}_{6} \mathrm{Cl}_{2}\), on hydrolysis gives a compound, that can reduce Tollen's reagent. The compound \(X^{\prime}\) isMHT CET 2009 Medium
- The period of revolution of planet A around the sun is 8 times that of planet B. How many times the distance of A from the sun is greater than that of B from the sun?MHT CET 2021 Medium