Number of strings over a set $A$ How can I calculate the number of strings of length $10$ over the set $A=\{a,b,c,d,e\}$ that begin with either $a$ or $c$ and have at least one $b$ ?
Is it accomplished through some sort of combinatorial logic coupled with discrete mathematics?

HINT


*

*Compute the $N$ number of such strings that begin with a or c.

*Compute the number of such strings that have no b.

*Compute the $M$ number of such strings that have at least one b from (2)

*Compute the $X$ number of such strings that have at least one b and begin with a or c.

*By inclusion/exclusion principle, you need $N+M-X$.

