This document provides an introduction to the topic of combinatorics. It discusses enumeration and graph theory as key aspects of combinatorics. Examples are given of factorial expressions, combinations, permutations, and sequences like arithmetic and geometric progressions. Common applications mentioned include loops and edges in graphs, as well as real world networks like maps, the internet, and social media.

2. ON THIS
LESSON,
YOU'LL
LEARN
ABOUT

3. COMBINATORICS

4. FOR EXAMPLE:
tastes—bitter, sour, salty, astringent, sweet,
hot—by taking them one at a time, two at a time,
three at a time, and so on

7. •Enumeration
•Graph theory

8. Enumeration
Graph theory

9. Factorials

10. n!/(n – m)!
!/(7 – 3)!
!/4!

11. Combination
nPr/r!
= n!/r! (n – r)!
5P3/3!
= 60/6
= 10

12. Probability number of
outcomes where A sits on the first chair/
total number of possible outcomes

14. the
difference between one term
and the next is a constant
d = 5 (the "common difference" between terms)
= 3 + 5(n−1)
= 3 + 5n − 5
= 5n − 2
x9 = 5×9 − 2
= 43

15. = 3 (the "common ratio" between terms)
x5 = 10×3^(5-1)
= 10×3^4
= 10×81
= 810

17. = 4 + 3(n−1)
= 4 + 3n − 3
= 3n + 1
x6 = 3×6 + 1
= 19

22. ✓Loops
✓Multiple edges
✓ Directed edges

23. ✓Google Map
✓The internet
✓Social media

24. THANK
YOU!