Module 8: Permutations, Combinations, and the Binomial Theorem

 

In Try This 4 you probably noticed that when you ignore the different colours of the L letters, there are half as many permutations. There are three distinguishable permutations of the letters LOL.

 

You may have discovered the way to calculate the number of permutations of n objects where r objects are identical, s objects are identical, t objects are identical, and so on is This formula is sometimes called the repetition formula.

 

Now go back and think about the example with Sara and Mark. Why did they get different answers even though they have the same number of letters in their names?

 

Since she has the letter a twice in her name, Sara has 12 arrangements. She could find the number of arrangements by using the repetitions formula Mark has no repeating letters, so the number of arrangements he can find is 4!, or 24.



textbook

To review another example of how permutations with repeating objects can be calculated, go to page 521 of the textbook and read the question and solution for part a. of “Example 3.”

 

 

The idea of repeated elements can be used in other permutation problems. One permutation problem is Try This 5.

 

Try This 5

 

After their math class, Sara and Mark go to Mark’s house to study for their upcoming math test. They wonder if they can use the math they learned in class to figure out the number of routes they have to choose from to get from the school to Mark's house if they only travel east and south. Mark’s house is four blocks east and two blocks south of the school. Can you help them out?

 

 

This is an image of a grid showing Mark’s house and the school.



textbook

If you need some help to answer Try This 5, read part b. of “Example 3” on page 521 of the textbook.