Suppose that six students, including Madhu and Puja, are having six beds arranged in a row. Further, suppose that Mudhu does not want a bed adjacent to Puja. Then the number of ways, the beds can be allotted to students is

Six X have to be placed in the squares of figure such that each row contains at least one X. The number of ways in which this can be done is:

Six people are going to sit in a row on a bench. A and B are adjacent,C does not want to sit adjacent to D.E and F can sit anywhere. Number of ways in which these six people can be seated is

A group of 2n students consisting of n boys and n girls are to be arranged in a row such that adjacent members are of opposite sex. The number of ways in which this can be done is

The 10 students of Batch B feel they have some conceptual doubt on Circular-permutation. Mr. Mathew called them in discussion room and asked them to sit down around a circular table which is surrounded by 13 chairs. Mr Mathew told that his (Mr. Mathew) adjacent seat should not remain the number of ways, in which the students can sit around a round table ifMr. Mathew also sit on a chair .

Six teachers and six students have to sit round a circular table such that thereis a teacher between any two students.The number of ways in which they can sit is