Answer: 12,620,256
Step-by-step 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 [tex]^{n+r-1}C_r=\ ^{31+8-1}C_{31}[/tex]
[tex]=^{38}C_{31}=\dfrac{38!}{31!(38-31)!}\\\\=\dfrac{38!}{31!7!}\\\\=\dfrac{38\times37\times36\times35\times34\times33\times32\times31!}{31!\times5040}\\\\=12620256[/tex]
Hence, the number of ways can a total inventory of 31 batteries be distributed among the eight different types = 12,620,256
