Consider three boxes, each containing $10$ balls labelled $1,2,....,10$. Suppose one ball is randomly drawn from each of the boxes. Denote by $n_i$, the label of the ball drawn from the $i^{th}$ box, ($i = 1, 2, 3$). Then, the number of ways in which the balls can be chosen such that $n_1 < n_2 < n_3$ is :
- 82
- 240
- 164
- 120
The Correct Option is D
Solution and Explanation
Top Questions on permutations and combinations
- How many different 4-letter words can be formed from the letters of the word "BINARY" without repetition?
- BITSAT - 2025
- Mathematics
- permutations and combinations
- The number of ways in which a cricket team of 11 members can be formed out of 6 batsmen, 6 bowlers, 4 all-rounders, and 4 wicket-keepers by selecting at least 4 batsmen, at least 3 bowlers, at least 2 all-rounders, and only one wicket-keeper is
- AP EAPCET - 2025
- Mathematics
- permutations and combinations
- All letters of the word `AGAIN' are permuted in all possible ways, and the words so formed (with or without meaning) are written as in a dictionary. Then the $50^{th}$ word is
- AP EAPCET - 2025
- Mathematics
- permutations and combinations
- The number of ways of forming the ordered pairs (p, q) such that p>q by choosing p and q from the first 50 natural numbers is:
- AP EAPCET - 2025
- Mathematics
- permutations and combinations
- If all possible 4-digit numbers are formed by choosing 4 different digits from the given digits $ 1, 2, 3, 5, 8 $, then the sum of all such 4-digit numbers is:
- AP EAPCET - 2025
- Mathematics
- permutations and combinations
Questions Asked in JEE Main exam
- A force of 49 N acts tangentially at the highest point of a sphere (solid of mass 20 kg) kept on a rough horizontal plane. If the sphere rolls without slipping, then the acceleration of the center of the sphere is:
- JEE Main - 2025
- Quantum Mechanics
Let \( A = \{-3, -2, -1, 0, 1, 2, 3\} \). A relation \( R \) is defined such that \( xRy \) if \( y = \max(x, 1) \). The number of elements required to make it reflexive is \( l \), the number of elements required to make it symmetric is \( m \), and the number of elements in the relation \( R \) is \( n \). Then the value of \( l + m + n \) is equal to:
- JEE Main - 2025
- Sets and Relations
For hydrogen-like species, which of the following graphs provides the most appropriate representation of \( E \) vs \( Z \) plot for a constant \( n \)?
[E : Energy of the stationary state, Z : atomic number, n = principal quantum number]- JEE Main - 2025
- Hydrogen
- Concentrated nitric acid is labelled as 75%by mass. The volume in mL of the solution which contains 30 g of nitric acid is: Given: Density of nitric acid solution is 1.25 g/mL.
- JEE Main - 2025
- Solutions
The largest $ n \in \mathbb{N} $ such that $ 3^n $ divides 50! is:
- JEE Main - 2025
- Number Systems
JEE Main Notification
Concepts Used:
Permutations and Combinations
Permutation:
Permutation is the method or the act of arranging members of a set into an order or a sequence.
- In the process of rearranging the numbers, subsets of sets are created to determine all possible arrangement sequences of a single data point.
- A permutation is used in many events of daily life. It is used for a list of data where the data order matters.
Combination:
Combination is the method of forming subsets by selecting data from a larger set in a way that the selection order does not matter.
- Combination refers to the combination of about n things taken k at a time without any repetition.
- The combination is used for a group of data where the order of data does not matter.