List of top Mathematics Questions on Combinations

A cricket team of 11 players from 16 players is to be selected. If three particular players are always included in the team, then the number of ways of selecting the team is

If six persons are to be selected to form a committee from a group of seven women and four men so that at least three women are there on the committee, then the number of ways it can be done, is

A box contains 24 identical balls of which one ball is black and the remaining balls are green. Three balls are taken simultaneously and randomly. The number of ways of getting only green balls, is

From a group of 10 persons, in how many ways can a selection of 4 persons to be made such that a particular person is always included?

There are twelve friends. On the eve of Diwali, they exchanged greeting cards among themselves. How many cards did they exchange altogether?

In Super 30 movie, Anand sir asks every of 30 students to do handshake among themselves, find total number of handshakes.

A regular polygon has 20 sides. The number of triangles that can be drawn by using the vertices but not using the sides are

A bag contains \( 5 \) red balls, \( 4 \) black balls, and \( 3 \) white balls. Then the number of ways of selecting three balls at random that contains at least one white ball is

If \[ \binom{n+2}{8} : \, \binom{n-2}{4} = 57 : 16, \text{ then } n \text{ is } \]

The value of $\displaystyle\sum_{r=0}^{22}{ }^{22} C_r{ }^{23} C_r$ is

Let 5 digit numbers be constructed using the digits $0,2,3,4,7,9$ with repetition allowed, and are arranged in ascending order with serial numbers Then the serial number of the number 42923 is

Suppose $\displaystyle\sum_{r=0}^{2023} r^{22023} C_r=2023 \times \alpha \times 2^{2022}$ Then the value of $\alpha$ is

Number of 4-digit numbers (the repetition of digits is allowed) which are made using the digits 1,2 , 3 and 5 , and are divisible by 15 , is equal to _____

The number of ways, 16 identical cubes, of which 11 are blue and rest are red, can be placed in a row so that between any two red cubes there should be at least 2 blue cubes, is _________.

If the sum of the coefficients of all the positive powers of x, in the Binomial expansion of \(\left(x^n+\frac{2}{x^5}\right)^7\) is 939, then the sum of all the possible integral values of n is ____________.

The value of $-{ }^{15} C _{1}+2 .{ }^{15} C _{2}-3 .{ }^{15} C _{3}+\ldots $ $-15 .{ }^{15} C _{15}+{ }^{14} C _{1}+{ }^{14} C _{3}+{ }^{14} C _{5}+\ldots .+{ }^{14} C _{11}$ is

From 4 men and 6 ladies a committee of five is to be selected. The number of ways in which the committee can be formed so that men are in majority is

If $^{n}C_{2017} = {}^{n}C_{2016}$, then $^{n}C_{4033}$ equals

Suppose that $20$ pillars of the same height have been erected along the boundary of a circular stadium. If the top of each pillar has been connected by beams with the top of all its non-adjacent pillars, then the total number beams is :

If \( ^nC_{r-1}=36, ^nC_r=84, ^nC_{r+1}=126 \), then \( n= \)

If \( nC_{r-1} = 36 \), \( nC_r = 84 \) and \( nC_{r+1} = 126 \), then the value of \( r \) is:

If \( ^nC_2 + ^nC_3 = ^6C_3 \) and \( ^nC_x = ^nC_3, x \neq 3 \), then the value of \( x \) is equal to: