A debate club consists of girls and boys. A team of members is to be selected from this club including the selection of a captain (from among these members) for the team. If the team has to include at most one boy, then the number of ways of selecting the team is
Two women and some men participated in a chess tournament in which every participant played two games with each of the other participants. If the number of games that the men played between them-selves exceeds the number of games that the men played with the women by, then the number of men who participated in the tournament lies in the interval
Let be two sets containing seven and three distinct elements respectively. Then the total number of functions that are onto, if there exist exactly three elements in such that is equal to:
In a tournament with five teams, each team plays against every other team exactly once. Each game is won by one of the playing teams and the winning team scores one point, while the losing team scores zero. Which of the following is NOT necessarily true?
A committee of member is to be formed from males and females. If is the number of ways the committee is formed with at least males and is the number of ways the committee is formed with at least females, then
Suppose that pillars of the same height have been erected along the boundary of 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 of beams is:
A man has friends, of them are ladies and are men. His wife also has friends, of them are ladies and are men. Assume and have no common friends. Then the total number of ways in which and together can throw a party inviting ladies and men, so that friends of each of and are in this party is:
Consider three boxes, each containing balls labelled . Suppose one ball is randomly drawn from each of the boxes. Denote by , the label of the ball drawn from the box, . Then, the number of ways in which the balls can be chosen such that is :
