Question1

a.8 sprinters compete in the Olympics. The first receives the gold medal, the second receives the silver medal, and the third receives the bronze medal. In how may ways these medals can be awarded? (We assume there are no ties.)

b. How many different 5-digit numbers can be formed from digits 1, 2, and 3?

c. The CS department needs to select a team of 4 students for a programming competition. There are 8 eligible students. In how many ways this team can be selected?

d. Little Tommy has five blocks, each having a different letter on top: A, B, C, D, and E, and he arranges them in a row to form 5-letter strings. How many strings can be formed from these blocks?

e. How many different strings can be formed in the previous question, if the blocks are labeled A, A, B, C, D, and E (that is, we have two blocks with label A)?