Question

There are 30 boys and 35 girls that try out for a chorus. The choir director will select 10 girls and 10 boys from the children trying out. How many ways are there for the choir director to make his selection?

Answer 1

Answer:

5.52 * 10^15 ways

Step-by-step explanation:

Given that there are 30 boys and 35 girls. The director will select 10 girls and 10 boys,

We use combinations when the question is on the number of ways of selecting objects  and the order of selection is not to be counted. Therefore, for this selection, the number of ways

= ³⁰C₁₀ × ³⁵C₁₀

= $\frac{30!}{(30-10)!10!} *\frac{35!}{(35-10)!10!}$

= $\frac{30!}{20!10!} *\frac{35!}{25!10!}$

= 30045015 * 183,579,396

= 5.51565 * 10^15

≈ 5.52 * 10^15 ways