High School Statistics Problem 14 (Awarding B.A.)?

How many ways can I choose 5 dogs and 4 cats out of a group of 10 dogs and 6 cats?

a] If repetition is permitted

b] If repetition is NOT permitted

Update:

I did 10C5*6C4 but I'm not sure if this accounts for the repetition

1 Answer

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  • 4 weeks ago
    Best Answer

    a]

    To choose s things out of a group of n things with repetition,

    no. of ways = ₛ₊ₙ₋₁Cₛ

    No. of ways to choose 5 dogs and 4 cats out of a group of 10 dogs and 6 cats if repetition is permitted

    = ₅₊₁₀₋₁C₅ × ₄₊₆₋₁C₄

    = ₁₄C₅ × ₉C₄

    = (14/9!5!) × (9!/5!4!)

    = 2002 × 126

    = 252,252

    b]

    To choose s things out of a group of n things WITHOUT repetition,

    no. of ways = ₙCₛ

    No. of ways to choose 5 dogs and 4 cats out of a group of 10 dogs and 6 cats if repetition is NOT permitted

    = ₁₀C₅ × ₆C₄

    = (10!/5!5!) × (6!/2!4!)

    = 252 × 15

    = 3,780

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