1. Whats the Difference?
"My fruit
salad is a
combination
of apples,
"The combination grapes and
to the safe was bananas"
472"

2. • We don't care what order the fruits are in, they
could also be "bananas, grapes and apples" or
"grapes, apples and bananas", its the same fruit
salad.
• Now we do care about the order. "724" would
not work, nor would "247". It has to be exactly
4-7-2.

3. In Maths we use precise
language..
• If the order doesn’t matter, it is a
COMBINATION
• If the order does matter, it is a
PERMUTATION

4. In Maths we use precise
language..
• If the order doesn’t matter, it is a
COMBINATION
• If the order does matter, it is a
PERMUTATION
A PERMUTATION IS AN ORDERED COMBINATION.

5. n
The ( ) Notation
r
n
• Can also be written as C aswell as nCr
r
and C(n,r).
• It gives the number of ways of choosing r
objects from n different objects.
• It is pronounced ‘n-c-r’ or ‘n-choose-r’.

6. How to Calculate It.
n) =
(r n! n) = n(n - 1)(n - 2)...(n - r +1)
(r
r! (n - r)! r!

7. How to Calculate It.
n) =
(r n! n) = n(n - 1)(n - 2)...(n - r +1)
(r
r! (n - r)! r!
Definition!

8. How to Calculate It.
n) =
(r n! n) = n(n - 1)(n - 2)...(n - r +1)
(r
r! (n - r)! r!
Definition! Practical!

9. You have a go!
n
0
n
n

10. You have a go!
• Question 3 on your
worksheet.
n
0
n
n

11. You have a go!
• Question 3 on your
worksheet.
• Answer 15.
n
0
n
n

12. You have a go!
• Question 3 on your
worksheet.
• Answer 15.
• And Question 4.
n
0
n
n

13. You have a go!
• Question 3 on your
worksheet.
• Answer 15.
• And Question 4.
• (a) (n) = 1
0
n
n

14. You have a go!
• Question 3 on your
worksheet.
• Answer 15.
• And Question 4.
• (a) (n) = 1
0
• (b) (n) = 1
n

15. Now a twist
• Assume you have 13 soccer players and
you can pick only 11 to play.
• How many ways can you choose those
players - Question 5.

16. • You can also find it this way!
• Think of it .. every time you choose 11 you
don’t choose 2!
• 13) = (13) = 13 × 12 = 78
Thus (12 2
2×1

17. The Twin Rule
n) = ( n)
• It states that ( r n-r
• Proof:
LHS = =
RHS = = n! = n! = LHS
(n - r)!(n - (n - r))! (n - r)!r!

18. Equations using
(n-c-r)
When you have to solve equations the
following are very usefull.
n n
(1) = 1 ( 2 ) = n(n - 1) = n(n - 1)
2×1 2

19. Example
• Solve for the value of the natural number n
n
such that ( ) = 28.
2

20. Solution
n(n - 1) = 28
2
n^2 - n = 28
2
n^2 - n = 28 -> n^2 - n - 28 = 0
(n - 8)(n + 7) = 0
n=8 n=-7
Reject n = - 7 is not a natural number.
Therefore n = 8.