Permutation Week 1

Suppose you are going to see your friends at Sampaloc Lake because you are going to spend one-hour bonding with them through biking. Sampaloc Lake is the most popular lake among the Seven Lakes in San Pablo City.

But you have a problem about the suit that you are going to wear. You need to make a decision by choosing among your 5 shirts, 3 pants, 2 rubber shoes and 4 socks.

Let us have illustrations by arranging them using the Tree Diagram.

We can also do this by Systematic Listing:

Fundamental Counting Principle 

During Fiesta, as one of our traditions, sweet delicacies are always present. Your mother prepares three types of these: Ubeng Halaya, Buko Salad, and Sweetened Macapuno.

If you are supposed to help your mother in preparing the dishes to be served to your visitors, then, in how many possible ways can you serve the three sweet delicacies?

As you can see from the Tree Diagram and Systematics Listing , There are 6 possible ways that you can serve the sweet delicacies.

Using the FCP(Fundamental Counting Principle

In this example you notice that the factors are decreasing. Another way of writing (3)(2)(1) is 3! ( read as 3 factorial ).

Permutations taken all at a time

Permutations taken r at time

Distinguishable Permutations

Circular Permutations