Permutations and Combinations

1.There are 30 balloons in the van, 10 of which are Blue, 11 are White, and 9 are Green. You will select 9 balloons from the van. Calculate:

(i). Suppose each of the 9 balloons that are selected will be given to a particular class. For example, balloon 1 could be given to Class A or to Class B or to Class C, etc. There are 9 classes. How many ways can the 9 balloons be selected from the 30? Carry out the arithmetic so that you have a single number as your answer:

2. You must show your work by setting up the problem using combinatorics. A group of students are playing a card game in the Johnson center. The game uses a standard, well-shuffled deck of 52 playing cards such as described in your textbook. A hand of cards consists of TEN of the cards. Find the number of different hands that :

(i). The hand consists of 4 of a kind, 2 of a different kind, and 4 of a different kind.