A camera shop stocks eight different types of batteries, one of which is type A76. Assume there are at least 30 batteries of each type. Required:
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?
c. How many ways can a total inventory of 30 batteries be distributed among the eight different types if the inventory includes at most three A7b batteries?

a. 10295472 ways

b. 4272048 ways

c. 6023424 ways

Step-by-step explanation:

Given that:

Camera shop stocks ----- 8 different types of batteries

one of which is ---- A76

Assume that 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.

The number of ways a total inventory of 30 batteries be distributed is :

= 10295472 ways

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?

If we must include 4  A76 batteries; then the number of ways a total inventory of 30 batteries can be distributed among eight different types of batteries will be:

30 - 4 = 26 batteries

Now;

= 4272048 ways

c. If we must include at most three A7b batteries. the number of ways that a total inventory of 30 batteries can be distributed among eight different types of inventory is:

= 1947792 + 1623160 + 1344904 + 1107568

= 6023424 ways