Permutations and Combinations (VCE)

Combinations and the relationship between permutations and combinations and problems involving restrictions.

LO: To calculate the number of different combinations and permutations from chance events.

Know:

  • How to construct an experiment
  • The definition of with and without replacement
  • Probability is a scale from 0 to 1.
  • Determine the probability of events.
  • The difference between Combinations and Permutations.

Understand:

  • the difference between combinations and permutations of chance events.

Do:

  • I can calculate the different combinations and permutations of chance events.

Factorial Notation

Mathematicians are generally pretty lazy. They like to find shortcuts to representing large calculations or sums, think indices! 

So they’ve developed factorial notation.

Factorial notation is basically the short form of multiplying a value by every number until it hits 1. For example, 5! means 5 x 4 x 3 x 2 x 1, but instead of writing 5 digits with multiplication signs, we can simplify it to a number with the ! sign.

Imagine having to write 100!

Permutations

Permutation basically is the act of rearranging the members of a set into a different order. It is different to combinations because the order does matter.

To put it into English terms, permutations are also similar to anagrams (rearranging the letters of a word to form new words). eg.) the letters of “listen” could be rearranged to spell “silent”, so silent is a permutation of listen.

The Permutation formula is pretty simple.

Basically, you have to find the factorial of the total items available then divide that number by the factorial of the difference between the total and number of items you’re picking.

Combination

Combinations are basically the number of ways that items can be arranged without taking into account the order.

For example, if I have 3 letters, ABC, and I wanted to find how many 2 letter combinations I could find then

The formula for calculating the number of combinations is the same as the permutation formula, but with an added piece which is adding in the k! piece when dividing by n!.

Permutation and Combination Videos