How many ways are there to distribute pens between two girls and one guy? There are two girls and one guy and 121 pens. How many ways are there to distribute pens between two girls and one guy, so that the girls have the same number of pens. The pens all are identical.
Please can you explain a bit more deeply?
Choose an even number $n\in[0,\dots,121]$.

Give $n/2$ pens to each girl, and $121-n$ pens to the boy.

There are $61$ even numbers between $0$ and $121$, hence $61$ ways to distribute the pens.
mathematical modelling of this situation is $2x + 2y = 120$ where
$x$ is the number of pens for a girl, and $2y + 1$ is the number
of pen for the boy. therefore $x + y = 60$ with $y$ ranging from
$0$ to $59$, then  the number of way to do this task is $60$