List of top Mathematics Questions on Combinatorics

दो पूर्णांक r व l लीजए जिनके लिए r $\ge$ l $\ge$ 3 है। ऐसे कितने फलन f : {1, 2, . . . r} $\rightarrow$ {1, 2, . . . r} हैं जिनके लिए f(1), f(2), . . . , f(l) सर्वथा अलग-अलग हैं?

Let $r, l$ be two integers such that $r \ge l \ge 3$. What is the total number of functions \[ f : \{1, 2, \dots, r\} \to \{1, 2, \dots, r\} \] such that $f(1), f(2), \dots, f(l)$ are all distinct?

Let \(A = \{ (a, b, c) : a, b, c \text{ are non-negative integers and } a + b + 2c = 22 \}\). Then \(n(A)\) is equal to:

Let \( p_n \) denote the total number of triangles formed by joining the vertices of an \( n \)-side regular polygon. If \( p_{n+1} - p_n = 66 \), then the sum of all distinct prime divisors of \( n \) is:

A building has ground floor and 10 more floors. Nine persons enter in a lift at the ground floor. The lift goes up to the 10th floor. The number of ways, in which any 4 persons exit at a floor and the remaining 5 persons exit at a different floor, if the lift does not stop at the first and the second floors, is equal to :

Two players A and B play a series of games of badminton. The player who wins 5 games first, wins the series. Assuming that no game ends in a draw, the number of ways in which player A wins the series is _________.

The number of elements in the set} \[ S=\left\{(r,k): k\in \mathbb{Z} \text{ and } {^{36}C_{r+1}}=\frac{6\left({^{35}C_r}\right)}{k^2-3}\right\} \] is:

\( T_m \) denotes the number of triangles that can be formed with the vertices of a regular polygon of \( m \) sides. If \( T_{m+1} - T_m = 15 \), then \( m = \)

A set contains 9 elements. Then the number of subsets of the set which contains at most 4 elements is:

In how many ways 11 identical toys be placed in 3 distinct boxes such that no box is empty?

In how many ways can 8 identical pens be distributed among Aal, Bal, and Cal so that Aal gets at least 1 pen, Bal gets at least 2 pens, and Cal gets at least 3 pens?

In how many ways 5 identical envelopes be placed among 3 distinct boxes such that any number of envelopes can be placed in any box.

Find the number of natural number solutions to \(a + b + c = 8\)

Find the number of whole number solutions to \(a + b + c = 8\)

The number of rectangles in a 6 $\times$ 6 grid is ______.

There are 4 horizontal and 4 vertical lines on a board. What is the maximum number of rectangles that can be formed?

In a car with seating capacity of exactly five persons, two persons can occupy the front seat and three persons can occupy the back seat. If amongst the seven persons, who wish to travel by this car, only two of them know driving, then the number of ways in which the car can be fully occupied and driven by them, is:

Number of non-negative integral solutions of the equation \[ a+b+2c=22 \] is

The number of non-negative integer solutions of the equation \[ a + b + 2c = 22 \] is:

Let \( A = \{1, 4, 7\} \), \( B = \{2, 3, 8\} \). Let \( R \) be a relation defined as \[ \{((a_1, b_1), (a_2, b_2)) \in (A \times B) \times (A \times B) : (a_2 + b_1) \text{ divides } (a_1 + b_2)\} \], then find the number of such relations.

Let \( A = \{2, 3\} \) and \( B = \{5, 6\} \), then the number of relations from \( A \times B \) to \( A \times B \) are:

If \( \lim_{x \to 0} \frac{1 - \cos(\alpha x)\cos((\alpha + 1)x)\cos((\alpha + 2)x)}{\sin^2((\alpha + 1)x)} = 2 \), then the product of all possible values of \( \alpha \) is:

Let \( f: A \to A \) be a function, where \( A = \{1, 2, 3, 4, 5, 6\} \). The number of one-one functions such that \( f(1) \le 3 \), \( f(3) \le 4 \) and \( f(2) + f(3) = 5 \), is:

A bag contains 4 red balls, 6 yellow balls and 5 blue balls. In how many ways we can select 8 balls such that we get at least two balls of each colour?