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?b. how many ways can a total inventory of 30 batteries be distributed among the eight different types if the inventory must include at least four a76 batteries?

Statistical Method

For A:

Given:

k = 30
n = 8

Solution:

where ! = factorial

the required number is:

C (30 + 8 - 1, 30) = C (37, 30)

=37! / (37 - 30)! (30)!
= 10295472

For B:

Given:

k = 26
n = 8

Solution:

the require number is:

C (26 + 8 -1, 26) = C (33,26)

= 33! / (33 - 26)! (26)!
= 4272048

The answers are 10295472 for (a) and 4272048 for (b)