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

Option: B is the correct answer.

B) 25

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=(n!)/((n-r)!r!)`

Hence, the value of
`8_C_1* 12_C_1* 5_C_1` is:

`=(8!)/((8-1)!1!)+(12!)/((12-1)!1!)+(5!)/((5-1)!1!)\\\\\\=(8!)/(7!)+(12!)/(11!)+(5!)/(4!)\\\\=8+12+5\\\\=25`

Hence, the number of combinations is:

25