Answer:
Option: B is the correct answer.
B) 25
Step-by-step explanation:
Joel is getting a dog, a cat, and a hamster.
He goes to the pet store and can choose from 8 dogs, 12 cats, and 5 hamsters.
i.e. the total number of combinations that are possible could be calculated with the help of Combination as:
[tex]8_C_1+12_C_1+5_C_1[/tex]
We know that:
[tex]n_C_r=\dfrac{n!}{(n-r)!r!}[/tex]
Hence, the value of [tex]8_C_1\times 12_C_1\times 5_C_1[/tex] is:
[tex]=\dfrac{8!}{(8-1)!1!}+\dfrac{12!}{(12-1)!1!}+\dfrac{5!}{(5-1)!1!}\\\\\\=\dfrac{8!}{7!}+\dfrac{12!}{11!}+\dfrac{5!}{4!}\\\\=8+12+5\\\\=25[/tex]
Hence, the number of combinations is:
25
