(n - r)! Examples: In a local swimming competition, there are 20 contestants. The first, second, and third placer will be awarded with gold, silver,...

N! (n - r)! Examples: 1. In a local swimming competition, there are 20 contestants. The first, second, and third placer will be awarded with gold, silver, and bronze medals, respectively. How many different possible competition results are there? 2. Three girls and nine boys are to be lined up to get in a bus. In how many ways can this be done if all the girls insist to be together? 3. In the previous example, suppose 2 of the boys (Mark and Jim) refused to be together. How many different arrangements are possible? 4. How many different ways can you sit 12 students in a round table? 5. How many different "words" can be made using all the letters of the word STATISTICS? 6. How many different ways can you distribute 20 candies to 5 kids? What if you have to give at least one candy to each kid?