# 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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- 冷眼旁觀Lv 64 weeks agoBest 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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Does your answer for 'B' account for order? (ie. does order matter?