The sum of all the four-digit numbers that can be formed using all the digits 2, 1, 2, 3 is equal to ______.
The sum of all the four-digit numbers that can be formed using all the digits 2, 1, 2, 3 is equal to ______.
Solution and Explanation
The number of four-digit numbers that can be formed using the digits 2, 1, 2, and 3 is \( \frac{4!}{2!} = 12 \).
These are the permutations of the digits 2, 1, 2, and 3. The sum of digits at the unit place is calculated as: \[ 3 \times 1 + 6 \times 2 + 3 \times 3 = 24. \] Now, the required sum is: \[ 24 \times 1000 + 24 \times 100 + 24 \times 10 + 24 \times 1 = 24 \times (1000 + 100 + 10 + 1) = 24 \times 1111 = 26664. \] Thus, the sum is \( 26664 \).
Top Questions on Permutations
- The number of numbers greater than $5000$, less than $9000$ and divisible by $3$, that can be formed using the digits $0,1,2,5,9$, if repetition of digits is allowed, is
- JEE Main - 2026
- Mathematics
- Permutations
- The letters of the word ``UDAYPUR'' are written in all possible ways with or without meaning and these words are arranged as in a dictionary. The rank of the word ``UDAYPUR'' is
- JEE Main - 2026
- Mathematics
- Permutations
- In a group of 3 girls and 4 boys, there are two boys \( B_1 \) and \( B_2 \). The number of ways in which these girls and boys can stand in a queue such that all the girls stand together, all the boys stand together, but \( B_1 \) and \( B_2 \) are not adjacent to each other, is:
- JEE Main - 2025
- Mathematics
- Permutations
- In how many ways can 5 people be arranged in a row?
- MHT CET - 2025
- Mathematics
- Permutations
- How many 4-digit numbers can be formed using the digits 1, 2, 3, 4, 5 without repetition such that the number is divisible by 5?
- BITSAT - 2025
- Mathematics
- Permutations
Questions Asked in JEE Main exam
Let \( ABC \) be a triangle. Consider four points \( p_1, p_2, p_3, p_4 \) on the side \( AB \), five points \( p_5, p_6, p_7, p_8, p_9 \) on the side \( BC \), and four points \( p_{10}, p_{11}, p_{12}, p_{13} \) on the side \( AC \). None of these points is a vertex of the triangle \( ABC \). Then the total number of pentagons that can be formed by taking all the vertices from the points \( p_1, p_2, \ldots, p_{13} \) is ___________.
- JEE Main - 2026
- Coordinate Geometry
- A voltage regulating circuit consisting of a Zener diode having breakdown voltage of $10\,\text{V}$ and maximum power dissipation of $0.4\,\text{W}$ is operated at $15\,\text{V}$. The approximate value of protective resistance in this circuit is ___ $\Omega$.
- JEE Main - 2026
- Semiconductor electronics: materials, devices and simple circuits
- Two point charges of \(1\,\text{nC}\) and \(2\,\text{nC}\) are placed at two corners of an equilateral triangle of side \(3\) cm. The work done in bringing a charge of \(3\,\text{nC}\) from infinity to the third corner of the triangle is ________ \(\mu\text{J}\). \[ \left(\frac{1}{4\pi\varepsilon_0}=9\times10^9\,\text{N m}^2\text{C}^{-2}\right) \]
- JEE Main - 2026
- Electrostatics
Consider the following two reactions A and B:
The numerical value of [molar mass of $x$ + molar mass of $y$] is ___.
- JEE Main - 2026
- Organic Chemistry
Consider an A.P. $a_1,a_2,\ldots,a_n$; $a_1>0$. If $a_2-a_1=-\dfrac{3}{4}$, $a_n=\dfrac{1}{4}a_1$, and \[ \sum_{i=1}^{n} a_i=\frac{525}{2}, \] then $\sum_{i=1}^{17} a_i$ is equal to
- JEE Main - 2026
- Arithmetic Progression
Concepts Used:
Permutations
A permutation is an arrangement of multiple objects in a particular order taken a few or all at a time. The formula for permutation is as follows:
\(^nP_r = \frac{n!}{(n-r)!}\)
nPr = permutation
n = total number of objects
r = number of objects selected
Types of Permutation
- Permutation of n different things where repeating is not allowed
- Permutation of n different things where repeating is allowed
- Permutation of similar kinds or duplicate objects