Question

A camera shop stocks eight different types of batteries, one of which is type A76. Assume there are at least 31 batteries of each type. (a) How many ways can a total inventory of 31 batteries be distributed among the eight different types

Answer 1

Answer: 12,620,256

Explanation:

Given: The camera shop socks eight different types of batteries and there re at least 31 batteries of each type.

Here we want to select r= 31 batteries from n= 8 kinds of batteries, then formula we use to find number of ways is
`^(n+r-1)C_r=\ ^(31+8-1)C_(31)`

`=^(38)C_(31)=(38!)/(31!(38-31)!)\\\\=(38!)/(31!7!)\\\\=(38*37*36*35*34*33*32*31!)/(31!*5040)\\\\=12620256`

Hence, the number of ways can a total inventory of 31 batteries be distributed among the eight different types = 12,620,256