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 differe

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

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Answers ( No )

    0
    2021-11-23T17:47:38+00:00

    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

    0
    2021-11-23T17:47:58+00:00

    The answer is B) 25

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