1. More Probability and Counting Friday, April 9, 2004

2. Permutations There are 6! permutations of the 6 letters of the word square. In how many of them is r the second letter? _ r _ _ _ _ In how many of them are q and e next to each other?

3. More Permutations How many different arrangements (permutations) are there of the digits 01234? How many 5-digit numbers can you make of those digits, in which the first digit is not 0? How many 5-digit odd numbers can you make?

4. License Plates License Plates in the State of Pennsylvania consists of 7 characters which may be letters or numbers. How many 7 character plates are possible?

5. Partitions A barrel contains 15 apples. Of the apples, 5 are rotten and 10 are good. Three apples are selected at random. What is the probability of selecting 2 good and 1 rotten apple?

6. More Partitions What is the probability of getting at least one rotten apple?

7. Binomial Theorem

8. Binomial Theorem Continued Use Pascal’s Triangle for Coefficients Write out the expansion of (a + b) 5

9. Assignment Homework #6 is posted – Due Friday, April 16 No Class Monday, April 12