Division and Distribution of Objects

How many different ways can $15$ Candy bars be distributed among Ram, Shyam, Ghanshyam and Balram, if Ram can not have more than $5$ candy bars and Shyam must have at least two. Assume all Candy bars to be alike.

In how many ways can $12$ different things be equally distributed among $4$ persons? If they are divided into $4$ groups instead of giving away to $4$ persons, what will be the number of ways?

In how many different ways can $15$ distinct objects be divided

into $3$ groups of $5$ objects each;

In how many different ways can $15$ distinct objects be divided
in $3$ groups of $4,5$ and $6$ objects;

A person has in his bag $14$ notes of $\mathrm{Rs}.100$ each, $9$ notes of $\mathrm{Rs}. 50$ each, $4$ notes of $\mathrm{Rs}. 20$ each and $7$ notes of $\mathrm{Rs}. 10$ each. In how many different ways can be donate to a poor fund?

There are $4$ ten-rupee, $5$ five-rupee and $3$ two-rupee notes. How many selections of at least one ten-rupee and one two-rupee notes are possible?

Find the number of factors (except $1$) of $420$, excepting the number itself.

In how many different ways the number $1440$ be expressed as the product of two factors (considering $1$ as a factor)?

How many different factors (except 1) are there of the numbers 

$1155$

How many different factors (except 1) are there of the numbers 

$113400$

How many different factors (except 1) are there of the numbers 
$546$ 

A Committee of $12$ is to be formed from $9$ women and $8$ men. In how many ways this can be done if at least $5$ women have to be included in a committee? In how many of these committees

The women are in majority?

Find the number of positive integral solutions of $x+y+z+w=20$ under the following conditions:

each variable is an odd number;

Find the number of positive integral solutions of $x+y+z+w=20$ under the following conditions:

$x, y, z$ and $w$ have different values ($0$ excluded).

Find the number of positive integral solutions of $x+y+z+w=20$ under the following conditions:

$0$ values of are excluded.

Find the number of positive integral solutions of $x+y+z+w=20$ under the following conditions:

$0$ values of $x, y, z$ and $w$ are included.

Number of ways in which $32$ identical blankets can be distributed among $4$ persons so that each of them gets number of blankets which are divisible by $2$ but not by $4$, is

The number of ways in which $10$ apples, $5$ oranges and $5$ mangoes can be distributed among three persons, each receiving none, one or more is :
(assume fruits of the same species to be identical)

In How many ways can $17$ persons depart from airbase in $2$ MIG and $3$ Mirage Fighter jet, given that $2$ particular persons Abhinandan and Jayant depart by same MIG, ($4$ persons can sit in a MIG and $3$ persons can sit in a Mirage)

The number of ways in which $10$ boys can be divided into $2$ groups of $5,$ such that two tallest boys are in two different groups, is equal to