Question

charity event participants there are 15 seniors and 19 juniors in a particular social organization. in how many ways can 5 seniors and 2 juniors be chosen to participate in a charity event? the number of ways that 5 seniors and 2 juniors can be chosen is

Explanation:

Step1: Calculate ways to choose seniors

Use combination formula $C(n,k)=\frac{n!}{k!(n - k)!}$, where $n = 15$ (number of seniors) and $k=5$ (number of seniors to choose). So $C(15,5)=\frac{15!}{5!(15 - 5)!}=\frac{15!}{5!×10!}=\frac{15\times14\times13\times12\times11}{5\times4\times3\times2\times1}=3003$.

Step2: Calculate ways to choose juniors

Use combination formula with $n = 19$ (number of juniors) and $k = 2$ (number of juniors to choose). So $C(19,2)=\frac{19!}{2!(19 - 2)!}=\frac{19!}{2!×17!}=\frac{19\times18}{2\times1}=171$.

Step3: Calculate total ways

By multiplication - principle, multiply the number of ways to choose seniors and juniors. Total ways $=C(15,5)\times C(19,2)=3003\times171 = 513513$.

Answer:

$513513$