Question

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. How many different combinations can he get? A) 3 B) 25 C) 75 D) 480

Answer 1

The answer is B) 25

Answer 2

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:

$8_C_1+12_C_1+5_C_1$

We know that:

$n_C_r=\dfrac{n!}{(n-r)!r!}$

Hence, the value of $8_C_1\times 12_C_1\times 5_C_1$ is:

$=\dfrac{8!}{(8-1)!1!}+\dfrac{12!}{(12-1)!1!}+\dfrac{5!}{(5-1)!1!}\\\\\\=\dfrac{8!}{7!}+\dfrac{12!}{11!}+\dfrac{5!}{4!}\\\\=8+12+5\\\\=25$

Hence, the number of combinations is:

25