Combinatorics ppt

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!