1. Ten employees at a company picnic are to stand in a row for a group photograph. In how many ways can this be done if
(a) All employees are happy to stand in any order?
(b) Cathy and John insist on standing next to each other?
(c) Cathy and John refuse to stand next to each other?
2. A committee of 6 persons is to be selected randomly from a group of 6 men and 9 women. It is assumed that "random" selection means that each outcome (i.e., committee of 6 people) is equally likely.
(a) What is the total number of 6 person committees that can be created from this group?
(b) Find the probability that the committee consists of all women.
(c) Find the probability that the committee consists of 4 men and 2 women.
3. A production lot of size 100 is known to be 10% defective. A random sample of 5 items is selected without replacement. Determine the probability that there will be no defective items in the sample.