JEE Mains · Maths · STD 11 - 6. permutation and combination
The total number of words (with or without meaning) that can be formed out of the letters of the word '\(DISTRIBUTION\)' taken four at a time, is equal to ...........
- A \(3733\)
- B \(3736\)
- C \(3734\)
- D \(3735\)
Answer & Solution
Correct Answer
(C) \(3734\)
Step-by-step Solution
Detailed explanation
We have \(III, TT, D, S, R, B, U, O, N\) Number of words with selection ( \(a, a, a, b)\) \(={ }^8 \mathrm{C}_1 \times \frac{4 !}{3 !}=32\) Number of words with selection \((a, a, b, b)\) \(=\frac{4 !}{2 ! 2 !}=6\) Number of words with selection ( \(a, a, b, c)\)…
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
- Let \(S={\theta \in\left(0, \frac{\pi}{2}\right): \sum_{m=1}^{9}}\) \(\sec \left(\theta+(m-1) \frac{\pi}{6}\right) \sec \left(\theta+\frac{m \pi}{6}\right)=-\frac{8}{\sqrt{3}}\) Then.JEE Mains 2022 Hard
- Let \(A=\left[\begin{array}{ll}x & 1 \\ 1 & 0\end{array}\right], x \in R\) and \(A^{4}=\left[a_{i j}\right] .\) If \(a_{11}=109,\) then \(a_{22}\) is equal toJEE Mains 2020 Hard
- The function \(f(x)=\frac{4 x^{3}-3 x^{2}}{6}-2 \sin x+(2 x-1) \cos x\)JEE Mains 2021 Hard
- In a game two players \(A\) and \(B\) take turns in throwing a pair of fair dice starting with player \(A\) and total of scores on the two dice, in each throw is noted. \(A\) wins the game if he throws a total of \(6\) before \(B\) throws a total of \(7\) and \(B\) wins the game if he throws a total of \(7\) before \(A\) throws a total of six The game stops as soon as either of the players wins. The probability of \(A\) winning the game isJEE Mains 2020 Hard
- If the center and radius of the circle \(\left|\frac{z-2}{z-3}\right|=2\) are respectively \((\alpha, \beta)\) and \(\gamma\), then \(3(\alpha+\beta+\gamma)\) is equal toJEE Mains 2023 Hard
- Let for two distinct values of \(p\) the lines \(y=x+p\) touch the ellipse \(\mathrm{E}: \frac{\mathrm{x}^2}{4^2}+\frac{\mathrm{y}^2}{3^2}=1\) at the points A and B . Let the line \(\mathrm{y}=\mathrm{x}\) intersect E at the points C and \(D\). Then the area of the quadrilateral \(A B C D\) is equal toJEE Mains 2025 Medium
More PYQs from JEE Mains
- Let \(f ( x )\) be a quadratic polynomial with leading coefficient \(1\) such that \(f(0)=p, p \neq 0\) and \(f(1)=\frac{1}{3}\). If the equation \(f(x)=0\) and \(fofofof (x)=0\) have a common real root, then \(f(-3)\) is equal to \(........\)JEE Mains 2022 Hard
- Let \(A =\{2,3,4\}\) and \(B =\{8,9,12\}\). Then the number of elements in the relation \(R=\left\{\left(\left(a_1, b_1\right),\left(a_2, b_2\right)\right) \in(A \times B, A \times B): a_1\right.\) divides \(b_2\) and \(a_2\) divides \(\left.b_1\right\}\) is:JEE Mains 2023 Medium
- The surface area of a balloon of spherical shape being inflated, increases at a constant rate. If initially, the radius of balloon is \(3\) units and after \(5\) seconds, it becomes \(7\) units, then its radius after \(9\) seconds isJEE Mains 2022 Medium
- If vertex of a parabola is \((2,-1)\) and the equation of its directrix is \(4 x-3 y=21\), then the length of its latus rectum isJEE Mains 2022 Easy
- The number of natural numbers, between 212 and 999 , such that the sum of their digits is 15 , isJEE Mains 2025 Medium
- Let \(f(x)=\lim _{\theta \rightarrow 0}\left(\frac{\cos \pi x-x^{\left(\frac{2}{\theta}\right)} \sin (x-1)}{1+x^{\left(\frac{2}{\theta}\right)}(x-1)}\right), x \in R\).
Consider the following two statements :
(I) \(f ( x )\) is discontinous at \(x =1\).
(II) \(f ( x )\) is continous at \(x =-1\). Then,JEE Mains 2026 Easy