In A Class Tournament When The Participants Were To Play One Game With Another, Two Class Players Fell Ill, Having Played 3 Games Each (not Played Between Them). If The Total Number Of Games Played Is 84, The Number Of Participants At The Beginning Was:

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 :

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 :

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

The number of distinct rational numbers x such that 0 < x < 1 and x = p/q, where p, q ∈ {1, 2, 3, 4, 5, 6}, is: