QUESTION 12. The combination of 11 things taken 8 at a time ( 11 C B) is exactly the same as 11 things taken 3 at a time (11 C 3). Explain why this is logical and not just a coincidence.

Suppose you have 11 books and you randomly pick 3 to take on vacation with you. How many ways can you do this?

Four salesmen play "odd man out" to see who pays for lunch. They each flip a coin, and if there is a salesman whose coin doesn't match the others he pays for lunch. To clarify, the "odd man" must get heads while the other three get tails OR he must get tails while the other three get heads. Of course, since it is possible for two men get heads and two men get tails, not all flips will result in finding an "odd man". If this occurs the salesmen would be forced to flip again. What is the probability that there is an "odd man" the first time they flip?

Discrete Math. I just need help understanding the set up. Part A is 100 ways and  Part B is 30,240