What happens if the items being arranged in a problem are not all different? Does this influence the number of permutations?
Sara and Mark are in math class and their teacher asks them to figure out how many different ways they can arrange the letters in their own names. Sara can only come up with 12 arrangements, but Mark can find 24 arrangements. They both have 4 letters in their name. Why did they get different answers? Is one student correct and one student incorrect?
Complete Try This 4 to explore why the same number of letters do not result in the same number of permutations.
Try This 4
A frequently used shorthand in texting is LOL. This acronym means “laughing out loud.”
- Using all letters from the phrase, form as many three-letter arrangements as possible.
- How many different arrangements do you see if you ignore the different colours in the arrangements?
- Why is there a difference between questions 1 and 2?
- What can you divide your answer from question 1 by to get the answer from question 2?
Save your responses in your course folder.