The number of ways to distribute 20 chocolates among three students such that each student gets atleast one chocolate is
- 22C2
- 19C2
- 19C3
- 22C3
The Correct Option is B
Solution and Explanation
x + y + z = 20; x, y, z ≥ 1
Therefore, the number of ways is 19C2
Top Questions on permutations and combinations
Match List-I with List-II
List-I List-II (A) \(^{8}P_{3} - ^{10}C_{3}\) (I) 6 (B) \(^{8}P_{5}\) (II) 21 (C) \(^{n}P_{4} = 360,\) then find \(n\). (III) 216 (D) \(^{n}C_{2} = 210,\) find \(n\). (IV) 6720
Choose the correct answer from the options given below:- CUET (UG) - 2025
- General Aptitude
- permutations and combinations
- The number of different 5 digit numbers greater than 50000 that can be formed using the digits 0, 1, 2, 3, 4, 5, 6, 7, such that the sum of their first and last digits should not be more than 8, is:
- JEE Main - 2025
- Mathematics
- permutations and combinations
- The total number of terms in the expansion of \((x + a)^{100} + (x - a)^{100}\) after simplification will be:
- LPUNEST - 2025
- Mathematics
- permutations and combinations
- How many 5-digit telephone numbers can be constructed using the digits 0 to 9, if each number starts with 67 and no digit appears more than once?
- LPUNEST - 2025
- Mathematics
- permutations and combinations
The number of 6-letter words, with or without meaning, that can be formed using the letters of the word MATHS such that any letter that appears in the word must appear at least twice, is $ 4 \_\_\_\_\_$.
- JEE Main - 2025
- Mathematics
- permutations and combinations
Questions Asked in JEE Main exam
Two light beams fall on a transparent material block at point 1 and 2 with angle \( \theta_1 \) and \( \theta_2 \), respectively, as shown in the figure. After refraction, the beams intersect at point 3 which is exactly on the interface at the other end of the block. Given: the distance between 1 and 2, \( d = 4/3 \) cm and \( \theta_1 = \theta_2 = \cos^{-1} \frac{n_2}{2n_1} \), where \( n_2 \) is the refractive index of the block and \( n_1 \) is the refractive index of the outside medium, then the thickness of the block is cm.
- JEE Main - 2025
- Refraction of Light
A bob of mass \(m\) is suspended at a point \(O\) by a light string of length \(l\) and left to perform vertical motion (circular) as shown in the figure. Initially, by applying horizontal velocity \(v_0\) at the point ‘A’, the string becomes slack when the bob reaches at the point ‘D’. The ratio of the kinetic energy of the bob at the points B and C is:
- JEE Main - 2025
- Kinetic Energy
- A vessel at 1000 K contains \( \text{CO}_2 \) with a pressure of 0.5 atm. Some of \( \text{CO}_2 \) is converted into \( \text{CO} \) on addition of graphite. If total pressure at equilibrium is 0.8 atm, then \( K_p \) is:
- JEE Main - 2025
- Equilibrium
Two light beams fall on a transparent material block at point 1 and 2 with angle \( \theta_1 \) and \( \theta_2 \), respectively, as shown in the figure. After refraction, the beams intersect at point 3 which is exactly on the interface at the other end of the block. Given: the distance between 1 and 2, \( d = \frac{4}{3} \) cm and \( \theta_1 = \theta_2 = \cos^{-1} \left( \frac{n_2}{2n_1} \right) \), where \( n_2 \) is the refractive index of the block and \( n_1 \) is the refractive index of the outside medium, then the thickness of the block is …….. cm.
- JEE Main - 2025
- Units and measurement
Let \( y^2 = 12x \) be the parabola and \( S \) its focus. Let \( PQ \) be a focal chord of the parabola such that \( (SP)(SQ) = \frac{147}{4} \). Let \( C \) be the circle described by taking \( PQ \) as a diameter. If the equation of the circle \( C \) is: \[ 64x^2 + 64y^2 - \alpha x - 64\sqrt{3}y = \beta, \] then \( \beta - \alpha \) is equal to:
- JEE Main - 2025
- Parabola
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.