List of top Mathematics Questions on Combinations asked in KEAM

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

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

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

The number of ways a committee of 4 people can be chosen from a panel of 10 people 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

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:

Let \( T_n \) denote the number of triangles which can be formed by using the vertices of a regular polygon of \( n \) sides. If \( T_{n+1} - T_n = 36 \), then \( n \) is equal to:

Let \( T_n \) denote the number of triangles which can be formed by using the vertices of a regular polygon of \( n \) sides. If \( T_{n+1} - T_n = 36 \), then \( n \) is equal to:

Let \( T_n \) denote the number of triangles which can be formed by using the vertices of a regular polygon of \( n \) sides. If \( T_{n+1} - T_n = 36 \), then \( n \) is equal to:

The value of $ \left( \frac{^{50}{{C}_{0}}}{1}+\frac{^{50}{{C}_{2}}}{3}+\frac{^{50}{{C}_{4}}}{5}+.... \right. $ $ \left. +\frac{^{50}{{C}_{50}}}{51} \right) $ is

The number of diagonals in a hexagon is