For the second part think this way.
Put a one in each variable.
That leaves four to put into four places.
.
How many solutions in non-negative integers are
there to the equation
w +x+y +z = 8?
and
How many solutions in positive integers?
I think for the first part i am just looking at the number of 8 element multisubsets of a 4 element set e.g (8+4-1) choose 8?
For the second part I am a bit confused,
thanks for any help
Hello, hmmmm!
How many solutions in non-negative integers are
there to the equation: . ?
Place 8 objects in a row, leaving a space before, after and between them.
. .
Place 3 "dividers" in any of the 9 spaces.
. .
. .
. .
. .
. .
For each of the three dividers, there are 9 choices for location.
There are: . non-negative solutions to the equation.
How many solutions in positive integers?
Place 8 objects in a row, leaving a space between them.
. .
Select three of the 7 spaces in which to insert the dividers.
. . There are: . ways.
There are 35 positive integer solutions to the equation.