There are men and two women participating in a chess tournament. Each participant plays two games with every other participant. If the number of games played by the men between themselves exceeds the number of games played between the men and the women by , then the value of is :
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:
There are sections in a question paper and each section contains questions. A candidate has to answer a total of questions, choosing at least one question from each section. Then the number of ways, in which the candidate can choose the questions, 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 :
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
Find the largest positive integer such that the number of integers in the set which are divisible by is equal to the number of integers which are divisible by or (or both).
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:
From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on the shelf so that the dictionary is always in the middle. Then the number of such arrangement is
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
If there are letters written to different people and envelopes addressed to them, then the number of ways in which these letters can be arranged so that no letter goes into its corresponding envelope is
We will say that a rearrangement of the letters of a word has no fixed letters if, when the rearrangement is placed directly below the word, no column has the same letter repeated. For instance, is a rearrangement with no fixed letters of . How many distinguishable rearrangements with no fixed letters does have? (The two are considered identical)
