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## Permutations and Combinations

### Mathematics

#### Previous Years Questions

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Consider 4 boxes, where each box contains 3 red balls and 2 blue balls. Assume that all 20 balls are distinct. In how ma...
JEE Advanced 2022 Paper 2 Online
In a high school, a committee has to be formed from a group of 6 boys M1, M2, M3, M4, M5, M6 and 5 girls G1, G2, G3, G4,...
JEE Advanced 2018 Paper 2 Offline
A debate club consists of 6 girls and 4 boys. A team of 4 members is to be select from this club including the selection...
JEE Advanced 2016 Paper 1 Offline
Six cards and six envelopes are numbered 1, 2, 3, 4, 5, 6 and cards are to be placed in envelopes so that each envelope ...
JEE Advanced 2014 Paper 2 Offline
Let $${{a_n}}$$ denote the number of all n-digit positive integers formed by the digits 0, 1 or both such that no conse...
IIT-JEE 2012 Paper 2 Offline
Let $${{a_n}}$$ denote the number of all n-digit positive integers formed by the digits 0, 1 or both such that no conse...
IIT-JEE 2012 Paper 2 Offline
The total number of ways in which 5 balls of different colours can be distributed among 3 persons so that each person ge...
IIT-JEE 2012 Paper 1 Offline
the number of seven digit integers, with sum of the digits equal to 10 and formed by using the digits 1, 2 and 3 only, i...
IIT-JEE 2009
Consider all possible permutations of the letters of the word ENDEANOEL. Match the statements / Expressions in Column I ...
IIT-JEE 2008
The letters of the word COCHIN are permuted and all the permutations are arranged in an alphabetical order as in an Engl...
IIT-JEE 2007
If the LCM of p, q is $${r^2}\,{r^4}\,{s^2}$$, where r, s, t are prime numbers and p, q are the positive integers then n...
IIT-JEE 2005 Screening
A rectangle with sides of lenght (2m - 1) and (2n - 1) units is divided into squares of unit lenght by drawing parallel ...
IIT-JEE 2005 Screening
The number of arrangements of the letters of the word BANANA in which the two N's do not appear adjacently is
IIT-JEE 2002 Screening
Let $${T_n}$$ denote the number of triangles which can be formed using the vertices of a regular polygon of n sides. If ...
IIT-JEE 2001 Screening
How many different nine digit numbers can be formed from the number 223355888 by rearranging its digits so that the odd ...
IIT-JEE 2000 Screening
A five-digit numbers divisible by 3 is to be formed using the numerals 0, 1, 2, 3, 4 and 5, without repetition. The tota...
IIT-JEE 1989
The value of the expression $$\,{}^{47}{C_4} + \sum\limits_{j = 1}^5 {^{52 - j}\,{C_3}}$$ is equal to
IIT-JEE 1982
Eight chairs are numbered 1 to 8. Two women and three men wish to occupy one chair each. First the women choose the chai...
IIT-JEE 1982
Ten different letters of an alphabet are given. Words with five letters are formed from these given letters. Then the nu...
IIT-JEE 1982
$${}^n{C_{r - 1}} = 36,{}^n{C_r} = 84\,\,and\,\,{}^n{C_{r + 1}} = 126$$, then r is :
IIT-JEE 1979

## Numerical

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The number of 4-digit integers in the closed interval [2022, 4482] formed by using the digits $$0,2,3,4,6,7$$ is _______...
JEE Advanced 2022 Paper 1 Online
In a hotel, four rooms are available. Six persons are to be accommodated in these four rooms in such a way that each of ...
JEE Advanced 2020 Paper 2 Offline
An engineer is required to visit a factory for exactly four days during the first 15 days of every month and it is manda...
JEE Advanced 2020 Paper 2 Offline
Five persons A, B, C, D and E are seated in a circular arrangement. If each of them is given a hat of one of the three c...
JEE Advanced 2019 Paper 2 Offline
Let |X| denote the number of elements in a set X. Let S = {1, 2, 3, 4, 5, 6} be a sample space, where each element is eq...
JEE Advanced 2019 Paper 2 Offline
The number of 5 digit numbers which are divisible by 4, with digits from the set {1, 2, 3, 4, 5} and the repetition of d...
JEE Advanced 2018 Paper 1 Offline
Words of length 10 are formed using the letters A, B, C, D, E, F, G, H, I, J. Let x be the number of such words where no...
JEE Advanced 2017 Paper 1 Offline
Let n be the number of ways in which 5 boys and 5 girls can stand in a queue in such a way that all the girls stand cons...
JEE Advanced 2015 Paper 1 Offline
Let $${n \ge 2}$$ be an integer. Take n distinct points on a circle and join each pair of points by a line segment. Colo...
JEE Advanced 2014 Paper 1 Offline
Let $${n_1}\, &lt; {n_2}\, &lt; \,{n_3}\, &lt; \,{n_4}\, &lt; {n_5}$$ be positive integers such that $${n_1}\, + {n_2}\,... JEE Advanced 2014 Paper 1 Offline Consider the set of eight vectors$$V = \left\{ {a\,\hat i + b\,\hat j + c\hat k:a,\,b,\,c\, \in \left\{ { - 1,\,1} \rig...
JEE Advanced 2013 Paper 1 Offline

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IIT-JEE 1982

## True or False

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The product of any r consecutive natural numbers is always divisible by r!
IIT-JEE 1985

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