Question: How many ways to make $m$ tasks done, given that there are $n$ people, each people is capable of doing from $0$ to $m$ tasks, many people can take over 1 tasks.
This can be express in a binary array size $n*m$
Beolow is one case.
Examples: $n=2, m=2$.
There are $9$ ways to make $m=2$ tasks done.
Let denote that $2$ people are $P1$ and $P2$, $2$ tasks are $T1$ and $T2$.
So, we can express $9$ cases in binary that make $T1; T2$ done
$0011$ means that $P1$ do nothing and $P2$ covers $2$ tasks. Apart from this, we have $8$ other ways: $1001; 0110; 1100; 0111; 1011; 1110; 1101; 1111.$
There are $7$ cases that does not take into accounts as follows:
in the last two cases $0101; 1010$ just only task $T1$ or $T2$ done.
Your help is highly appreciated! Thanks a lot in advance!