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 ?

Six pictures are to be arranged from left to right on a wall of an art gallery for display. How many 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 ?

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 ?

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?

The letters of the word ‘TUESDAY’ are arranged in a line, each arrangement ending with letter S. How many different arrangements are possible ? How many of them start with letter D ?

A biologist studying the genetic code is interested to know the number of possible arrangements of 12 molecules in a chain. The chain contains 4 different molecules represented by the initials A (for Adenine), C (for Cytosine). G (for Guanine) and T (for Thymine) and 3 molecules of each kind. How many different such arrangements are possible in all ?

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 ?

From 6 different novels and 5 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on a shelf so that the dictionary is always in the middle. Then the number of such arrangements is :

The digits, from 0 to 9, are written on slips of paper and placed in a box. Three of the Slips of paper are drawn and placed in order. How many different outcomes are possible ?

A committees of 3 persons is to be constituted from a group of 2 men and 3 women. In how many ways can this be done ? How many of these committees would consist of 1 man and 2 women ?