Question

a science class consists of 14 boys and 15 girls. which expression can you use to find the number of ways the teacher can choose 5 girls to present their reports on monday and 5 boys to present their reports on tuesday? (₂₉p₅)(₂₄p₅) (₁₅p₅)(₁₄p₅) (₂₉c₅)(₂₄c₅) (₁₅c₅)(₁₄c₅)

Explanation:

Step1: Calculate ways to choose girls

We use combination formula $_{n}C_{r}=\frac{n!}{r!(n - r)!}$. There are 15 girls and we want to choose 5. So number of ways is $_{15}C_{5}=\frac{15!}{5!(15 - 5)!}$.

Step2: Calculate ways to choose boys

There are 14 boys and we want to choose 5. Using combination formula, number of ways is $_{14}C_{5}=\frac{14!}{5!(14 - 5)!}$.

Step3: Find total ways

By multiplication - principle, total number of ways to choose 5 girls and 5 boys is the product of number of ways to choose girls and number of ways to choose boys, i.e., $(_{15}C_{5})(_{14}C_{5})$.

Answer:

$(_{15}C_{5})(_{14}C_{5})$