Fundamental counting principle

Suppose you want to know how many combinations of looks you can do with the set of clothes that you have, what mathematical solution do you think you can use so you don’t have to mentally count all of the possible outcomes? How about, if you want to know how many kinds of arrangement you can do with the chairs in the classroom? In order to solve these problems you will need to know about permutations and combinations.

This chapter will have nine parts which will help us understand the basic concept of permutation and combination. In the first part of chapter, we will discuss about the fundamental counting principle. This principle states that if two separate events have m and m possible outcomes respectively, then the combined possible outcome for the combined events would be equivalent to m x n.

In the second part of this chapter will review how to write and solve a factorial notation. For example, if you are asked to solve four factorial or 4!, then you know that you need to solve for 1 x 2 x 3 x 4. Factorial notations are used throughout our discussion in this chapter like in proceeding parts of the chapter that focuses on path counting, and the difference between permutation and combination.

For the eighth this chapter, we will look into the application of all the concepts about permutations and combinations with that of the Pascal's triangle. If you want to know the answer for the question “what is a Pascal’s triangle?” you can check on it on various resources online.

Finally, in the last part of the chapter, we will look into the Binomial theorem. This theorem is used to find any power of a certain binomial without the need to multiply a long list of terms.

Fundamental counting principle

The fundamental counting principle can be very helpful when you need to figure out the possible number of outcomes of multiple events. The principle essentially works like this: If there are m possible ways for an event to occur, and n possible ways for another event to occur, there are m x n possible ways for both events to occur. In this lesson, we will apply the principle to real-life scenarios to see how it works.


    • a)
      How many pieces of clothing are you bringing all together?
    • b)
      If an outfit consists of a shirt and a pair of pants, how many different sets of outfit can you make?
      Determine the answer by using:
      (i) a tree diagram
      (ii) the fundamental counting principle
  • 5.
    How many odd four digit numbers are there? An example of a four digit number is 3581, while 0492 is a three digit number.
  • 6.
    Use only the digits 2, 4, 5, 6, 7, 8 and 9 to produce four digit numbers.
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Fundamental counting principle

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