List of top Mathematics Questions on Combinations

In a business meeting, each person shakes hands with each other person once. A person arrives after 5 people have left and he shakes hands only with those present. If the total number of handshakes is exactly 100, then the initial number of people in the party, is

In an election, the number of candidates is one more than the number of seats. If a voter can cast his vote in 30 ways, find the number of candidates (when a voter can cast his vote for one or more seats).

The product of first \( n \) odd natural numbers is :

Five candidates are contesting an election, and three members are to be elected. A voter can vote for any number of candidates, but not more than the number of members to be elected. The number of ways a person can cast their vote is :

The exponent of 7 in \( ^{100}C_{50} \) is :

If $^{n}C_{12} = ^{n}C_{8}$, then $^{n}C_{17} =$

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.

If \( n^+ C_{n+1} - n^3 C_n = 15(n + 2) \), then \( n = \)

There are 11 points in a plane of which 5 points are collinear. Then the total number of distinct quadrilaterals with vertices at these points is ______.

The number of ways in which a team of 11 players can be formed out of 25 players, if 6 out of them are always to be included and 5 of them are always to be excluded, is ______.

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

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

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 _____

Let \(T_n\) be the number of all possible triangles formed by joining vertices of an \(n\)-sided regular polygon. If \[ T_{n+1}-T_n=10, \] then the value of \(n\) is

If \[ {}^{9}C_3+{}^{9}C_5={}^{10}C_r \] for some \(r\in \mathbb{N}\), then \(r=\)