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 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 ?

It is required to seat 5 men and 4 women in a row so that the women occupy the even places. How many such arrangements are possible ?

In how many ways can 5 girls be seated in a row so that two girls Ridhi and Sanya are always together?

When a group photograph in taken, all the seven teachers should be in the first row and all the twenty students should be in second row, If the two corners of the second row are reserved for the two tallest students, interchangeable only between them and if the middle seat of the front row is reserved for the principal, how many arrangements are possible?

Find the number of arrangements of the letters of the word ‘INDEPENDENCE’. In how many of these arrangements, do all the vowels always occur together ?

In how many ways can 5 children be arranged in a line such that : two of them, Ram and Shyam are always together?

The students in a class are seated according to the marks in the previous examination. Once it so happens that four of these students get equal marks and therefore the same rank. To decide their seating arrangement, the teacher wants to write down all possible arrangements, one in each of separate bits of paper, in order to choose one of these by lots. How many bits of paper are required ?

There are 25 students in a class in which 15 boys and 10 girls. The class teacher select either a boy or girl for monitor of the class. In how many ways the class teacher can make this selection?

Find the numbers of ways in which 5 girls and 5 boys can be arranged in a row if no two boys are together.

In a class there are 30 boys and 18 girls. The teacher wants to select one boy and one girl to represent the class for a quiz competition. In how many ways can the teacher make this selection ?