Let A be The Set Of 4-digit Numbers A1a2a3a4 where A1 > A2 > A3 > A2 then n (A) Is Equal To :

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 :

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:

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:

The numbers of number of 9 different nonzero digits such that all the digits in the first four places are less than the digit in the middle and all the digits in the last four places are greater than that in the middle is :