Problem 1: a. Choose 4 shoes from 10 pair of shoes such that there is no matching pair of shoes. How many choices are there?

b. Choose 5 digits from 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 without replacement to from a five digit number. How many different ways to form an odd number are there?

Hint: A five-digit number does not start with 0.

Problem 2: Two people X and Y play ping-pong. They continue playing until either X or Y wins four games. How many different cases are possible?

Problem 3: Refer to the class example 56, slide 86 in probability. A labor dispute has arisen concerning the distribution 20 laborers to four different construction jobs:

1^st job (undesirable) required 6 laborers

2^nd required 4 laborers

3th required 5 laborers

4^th required 5 laborers

a. What is the probability that an ethnic group member is assigned to each type of job?

b. What is the probability that no ethnic group member is assigned to a type 4 job?