A sample of 4 people is selected from a group of six people

A sample of 4 people is selected from a group of six people named Ali, Bina, Chris, David, Erin and Frank.

4. How many such samples are possible?

5. What is the probability a sample containing Bina and Chris is selected.

6. How many different simple random samples of size 8 can be selected from a population consisting of 70 people? (you may use the combinations)

There are 6C4 = 15 such samples. [answer]

If Bina and Chris are already selected, then we can choose 4C2 = 6 ways for the other two people.

Thus,

P(with Bina and Chris) = 6/15 = 0.4 [answer]

There are 70C8 = 9440350920 ways [answer]