Question

1- How many ways are there to select a committee of 50% of 16 from 80% of the 110 people and select 50% of 16 for separate positions from 20% of 110 people

please with all the steps.

Answer 1

50% of 16=8 80% of 110=88 20% of 110=22

so if you simplify the question you will get:

How many ways are there to select a committee of 8 from 88 people and select 8 for separate positions from 22 people.

Now, the number of ways of selecting 8 people from 88= and the number of ways of selecting 8 people from 22=

so total number of ways=

Answer 2

Problem Breakdown:

1. First Group (80% of 110 people):

• Number of people = $0.8\times 110=88$.

• Committee size = $0.5\times 16=8$.

• Ways to choose:

  $$\left(\genfrac{}{}{0px}{}{88}{8}\right)$$

2. Second Group (20% of 110 people):

• Number of people = $0.2\times 110=22$.

• Committee size = $0.5\times 16=8$.

• Ways to choose:

  $$\left(\genfrac{}{}{0px}{}{22}{8}\right)$$

3. Total Ways:
   Multiply the two combinations (since selections are independent):

   $$\text{Total}=\left(\genfrac{}{}{0px}{}{88}{8}\right)\times \left(\genfrac{}{}{0px}{}{22}{8}\right)$$

Final Answer:

$$$$

Note:

• $\left(\genfrac{}{}{0px}{}{n}{k}\right)$ = "n choose k" = $\frac{n!}{k!(n-k)!}$.

• No simplification needed unless numerical values are required.