Question

Please answer the following combinatorics questions. Please write your answers as whole numbers (e.g., "4").

• How many ways can you order 7 people?  
• I have 12 different soccer balls, but I'm only going to take 2 of them to the game. How many different sets of 2 are possible where order does not matter?  
• A professor has a test bank with 8 different questions in it, for a particular group of questions on her test, she will only ask 3 of them and in a random order. How many different ways are there to order 3 questions out of the 8?  
• A university undergraduate degree program has 24 different classes an undergraduate can take this semester as an elective, though she will only take 3 of them. How many different combinations of 3 classes of the 24 can she take?  

Answer 1

• I can order 7 people in 7! Ways that is 5040
• I have 12 different soccer balls, but I'm only going to take 2 of them to the game. There are 12C2 ways to select it. That is there are 66 ways to select it.
• A professor has a test bank with 8 different questions in it, for a particular group of questions on her test, she will only ask 3 of them and in a random order. There are 8P3 different ways are there to order 3 questions out of the 8. That is there are 336 ways to ask 3 questions out of 8.
• A university undergraduate degree program has 24 different classes an undergraduate can take this semester as an elective, though she will only take 3 of them. She can take 24C3 different combinations of 3 classes of the 24 that is 2024 combinations are available.