Eight children are to be seated on a bench. How many arrangements are possible if the youngest child sits at the left hand end of the bench ?

Eight children are to be seated on a bench. In how many ways can the children be seated ?

A family consists of a grandfather, 5 sons and daughters and 8 grand child. They are to be seated in a row for dinner. The grand children wish to occupy the 4 seats at each end and the grandfather refuses to have a grandchild on either side of him. In how many ways can the family be made to sit?

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 ?

Three married couples are to be seated in a row having six seats in a cinema hall. If spouses are to be seated next to each other, in how many ways can they be seated ? Find also the number of ways of their seating if all the ladies sit together.

A committee of 11 members sits at a round table. In how many ways can they be seated if the 'President' and the 'Secretary' choose to sit together?

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 ?

Four men and four women sit to dine at a round table. In how many ways can they seat themselves so that no two women are together ?

In how many ways can be letters of word 'ASSASSINATION' be arranged so that: the arrangements be such that they start with O and end with T?

In how many ways can the letters of the word PERMUTATIONS be arranged if the words start with P and end with S?