Three boys and three girls are to be seated around a table in a circle. Among them, the boy X does not want any girl neighbour and the girl Y does not want any boy neighbour. How many such arrangements are possible ?

A teacher wants to arrange 5 students on the platform such that the boy ‘YUSUF’ occupies the first position and the girls ‘GEETA’ and ‘SEETA’ are always together. How many such arrangements are possible ?

Three boys and two girls stand in a queue. The probability, that the number of boys ahead is at least one more than the number of girls ahead of her, is

From a class of 12 boys and 10 girls, 10 students are to be chosen for a competition, at least including 4 boys and 4 girls. The 2 girls who won the prizes last year should be included. In how many ways can the selection be made ?

There are three prizes to be distributed among 6 students. In how many ways can this be done when no boy gets more than one prize.

There are three prizes to be distributed among 6 students. In how many ways can this be done when there is no resrtiction as to the number of prizes that a boy may get.

In how many different ways can five boys and five girls form a circle such that the boys and girls alternate?

In how many ways can 6 girls and 4 boys be seated in a row so that no two boys are together?

20 % of 25 students in a class are boys.How many girls are in the class?

There are three prizes to be distributed among 6 students. In how many ways can this be done when no boy gets all prizes.

Let the mirror image of the point A(5, 6) with respect to the line 2x + 3y = 15 be the point B. Find the equation of the circle described on AB as diameter. AC is any chord of the circle meeting the x-axis at D such that AD = 10DC. How many such chords are possible ?