combinatorics problem

[drufae]

in how many ways can the equation

 

[math] x_1 + x_2 + x_3 ......+ x_n = c[/math]

 

be solved for integer solutions.

 

This apparently uses the multinomial coefficients.though I could not understand how .

 

Also, what are the solutions if [math]x_1[/math] has constraint on it like

< 10,etc.

thanks in advance.