Question

q) A camera shop stocks eight different types of batteries, one
of which is type A7b. Assume there are at least 30 batteries
of each type.

a. How many ways can a total inventory of 30 batteries be
distributed among the eight different types?

Answer 1

This equals the number of ways where we choose 30 things (r=30) given we have 8 different types of objects (n=8). This equals the number of 30-combinations from 8 objects where repetition is allowed.

This number is:

$\bigl(\begin{smallmatrix} 30+8-1\\ 8-1 \end{smallmatrix}\bigr)=\bigl(\begin{smallmatrix} 37\\7 \end{smallmatrix}\bigr)$