There are five round stickers, 3 of them are red and the other two are green. It is desired to make a design by pasting them in a row. How many such designs are possible ?

It has been decided that the flag of a newly formed forum will be in the form of three blocks, each coloured differently. If there are six colours on the whole to choose from, how many designs 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 ?

In how many ways can 5 boys and 3 girls sit in a row so that no two girls are together ?

In an examination hall, there are four rows of chairs. Each row has 8 chairs one behind the other. There are two classes sitting for the examination with 16 students in each class. It is desired that in each row, all students belong to the same class and that no two adjacent rows are allotted to the same class. In how many ways can these 32 students be seated?

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?

If there are 12 persons in a party, and if each two of them shake hands with each other, how many handshakes happen ?

In how many ways can 4 boys and 3 girls be seated in a row so that no two girls are together ?

There are two identical balls of same material ,one being solid and the other being hollow. How will you distinguish them without weighing?

You have been provided with three test tubes one of them contains distilled water and the other two contain an acidic solution and a basic soution respectively . If you are given only red litmus paper, how will you identify the contents of each test tube?

Twelve cells each having the same e.m.f are connected in series and are kept to a closed box. Some of the cell are connected in reverse order .The battery is connected in series with an ammeter an external resistance R and two cells of the same type as an in the battery .The current when they and support each other is 3 ampere and current is 2 ampare when the two oppose each other. How many cells are connected in servese order ?