Combinatorics and counting: previous year questions
Asked 24 times in 5 exams across 10 years. Newest first.
Practise Combinatorics and counting, easy to hard →
Permutations and combinations
Counting arrangements and selections, with and without restrictions.
- CUET-PG 2024 Q56In how many ways can 10 economists attending a conference be accommodated in 2 triple sharing and 2 double sharing hotel rooms?
- UoH 2020 Q64Five persons namely, Bhaskar, Mary, Apala, Nemichand and Shahid are to be seated on five seats in a row such that Shahid and Bhaskar must sit next…
- UoH 2015 Q79Four persons namely, David, Anwar, Nazma and Rita are to be seated in a row such that David and Anwar must sit next to each other and Rita and Nazma…
- DSE 2013 Q15A certain club consists of 5 men and 5 women. A 5-member committee consisting of 2 men and 3 women has to be constituted. How many ways are there of…
- UoH 2013 Q844 first year and 3 second year students are to be seated in a row for their respective examinations in a manner that no two students from the same…
- DSE 2012 Q13An n -gon is a regular polygon with n equal sides. Find the number of diagonals (edges of an n -gon are not considered as diagonals) of a 10 -gon.
- JNU 2012 Q51If you count from 1 to 100, how many 7s will you pass on the way?
- JNU 2011 Q54In a certain country telephone numbers have 8 digits. The first two digits are the area code and are the same within a given area. The last 6 digits…
- JNU 2011 Q73How many 4-digit numbers can be formed, if no digit is used more than once?
- JNU 2011 Q74How many of the 4-digit numbers can be formed, if no digit is used more than once, which are divisible by 5?
- JNU 2010 Q78There are four bus routes between A and B and three bus routes between B and C. A man can travel round trip in number of ways by bus from A to C via…
- DSE 2009 Q1There are 4 married couples in a club. A 3-member committee must be formed from among them, such that no married couple is part of the committee.…
Inclusion-exclusion and complementary counting
Counting by adding and removing overlaps, or by counting what is not wanted.
- IIT JAM 2024 Q45There are 32 students, each taking at least one of English, Hindi, Mathematics. 16 take English, 8 Hindi, 18 Mathematics; 4 take English and Hindi…
- CUET-PG 2021 Q51If A and B are two sets such that n(A)=20, n(B)=35 and n(A∪ B)=50, then n(A∩ B) is equal to
- UoH 2015 Q86In a class of 50 students, 33 are Telugu speaking, 15 are Urdu speaking and 9 speak neither Telugu nor Urdu. How many students are both Telugu…
- DSE 2013 Q44A club consists of 5 men and 5 women. A 5-member committee of 2 men and 3 women has to be constituted. Suppose Mrs. F refuses to work with Mr. M.…
- JNU 2013 Q82In an election, half the electors voted for candidate A and two-thirds voted for candidate B. 10 electors voted for both A and B. 6 electors voted…
- UoH 2013 Q83Number of students who opted for econometrics course or game theory course is equal to 45. It is found that 25 students have taken both the courses…
- JNU 2010 Q36In an examination, there are three multiple-choice questions and each question has 4 choices. Number of ways in which a student can fail to get all…
Binomial coefficients and counting functions
Binomial expansions and counting maps between finite sets.
- CUET-PG 2022 Q43The number of terms in the expansion of the binomial distribution (a + b)⁴ is
- DSE 2021 Q4Find the value of Σᵣ₌₀⁵⁰ C(100, 2r). (Notation: C(a, b) denotes a choose b .)
- DSE 2015 Q53Let S have n>1 elements and A₁,…,Aₘ⊆ S satisfy: for any x≠ y in S, some Aᵢ contains exactly one of them. Then necessarily
- JNU 2015 Q7The binomial theorem states that
- JNU 2013 Q81Let set A contains m elements and set B contains n elements. Then the number of distinct functions from set A to set B which can be constructed is