A Father With 8 Children Takes 3 At A Time Go To The Zoological Garden, As Often As He Can Without Taking The Same 3 Children Together More Than Once. The Number Of Times He Will Go To The Garden Is :

In how many ways can 12 books be equally distributed among 3 students?

10 different toys are to be distributed among 10 children. Total number of ways of distributing these toys so that exactly 2 children do not get any toy, is equal to:

There are 20 persons among whom are two brothers. Find the number of ways in which we can arrange them around a circle so that there is exactly one person between the two brothers.

In how many ways can a party of 4 men and 4 women be seated at a circular table so that no two women are adjacent?

There are 5 gentlemen and 4 ladies to dine at a round table. In how many ways can they seat themselves so that no two ladies are together?

Find the number of ways in which 8 different flowers can be strung to form a garland so that 4 particular flowers are never separated.

How many integral solutions are there to x + y + z + t = 29, when x ≥ 1, y≥ 2, z ≥ 3 and t ≥ 0?

How many integral solutions are there to the system of equations

x₁ + x₂ + x₃ + x₄ + x₅ = 20 and x₁ + x₂ + x₃ = 5 when x_k ≥ 0?

There are n points in a plane of which no three are in a straight line except ‘m’ which are all in a straight line. Then the number of different quadrilaterals, that can be formed with the given points as vertices, is :

The number of divisors a number 38808 can have, excluding 1 and the number itself is :