In how many ways can 6 beads of same colour form a necklace ?

There are five colleges in a city. In how many ways can a man send 3 of his sons to a college, if no two of his sons are to read in the same college ?

In how many ways can a tissue grow in size?

In how many ways can 8 students be seated in : a line ?

Consider 21 different pearls on a necklace. How many ways can the pearls be placed in on this necklace such that 3 specific pearls always remain together?

In how many ways can a team of 3 boys and 3 girls be selected from 5 boys and 4 girls?

In how many ways can the following diagram be coloured subject to the following conditions ? No two adjacent regions receive the same colour .

In how many ways can the following diagram be coloured subject to the following conditions ? Each of the smaller triangle is to be painted with one of the three colours, red, blue or green.

Out of 5 men and 2 women a committee of 3 is to be formed. In how many ways can it be formed if at least one woman is to be included ?

In how many ways, we can choose two teams of mixed double for a tennis tournament from four couples such that if any couple participates, then it is in the same team?