This lesson is being recorded

1.

This lesson is
being
recorded

2.

Permutations
In how many ways can the letters of the word BEAUTY be
arranged?
360
5!
6!
7!

3.

Permutations
For the word BEAUTY, if the vowels are always together then how
many types of arrangement are possible?
4! X 3!
6!
4!
4! X 3

4.

5.

Year 12 Mathematics
Explore 1

6.

Learning objectives
Understand the different formulae used for permutations and
combinations
Be able to apply the correct formula in most situations
Be able to apply the correct formula in all situations

7.

Example 1
I should be one of the judges! When I heard the 16
songs in the competition, I knew which ones I thought
were the best. Last night they announced the results
and I had picked the same three songs in the same
order as the judges
What is the probability of her results?
The winner can be chosen in 16 ways, the second song can be chosen in 15
ways, the third song can be chosen in 14 ways.
The total number of ways of placing three songs in the first three positions is
16 x 15 x 14 = 3360
So the probability that her results are correct is

8.

Example 2
Consider a word ‘YOURSELVES’. In how many ways the letter can be
arranged if U and S always come together and ‘U’ always precedes ‘S’?
Solution: The word ‘YOURSELVES’ has 11
letters out of which ‘S’ repeats two times and
‘E’ repeats three times. The rest are all
different.
If the letter ‘U’ and ‘S’ come together, they
are considered as one letter.
The 10 letters can rearrange themselves in
10! = 3 628 800 ways.
Using the formula gives us = 302400 ways.