1. When do we add and when do we multiply?

2. How many ways can we draw a king or a seven from a deck? There are 4 kings and 4 sevens. Each of these cards satisfies the event. So, 4 + 4 = 8 How many ways can we draw a king and a seven from a deck? There are 4 kings to draw first, then for each king, there are 4 sevens that can match with it. Each event has a pair. So, 4 X 4 = 16

3. Combinations

4. Election #1 How many ways can a President, Vice President, and Secretary be selected from 4 people? PVP S 432 n = 4 X 3 X 2 = 24 This is a Permutation

5. Election #2 How many ways can a three person general council be created from four people? GC 432 One selection process (using permutations) could have resulted in: JohnMary Susan

6. Another selection could be: Mary SusanJohn Or: Susan MaryJohn If all that is being generated are groups of three, then there is no difference between these… (Like drawing a 5 card poker hand..)

7. The permutation counting technique counts every order. Order does not matter when a general group (or Subset) is being selected. Therefore, we can not use permutations when the order of the selected items does not matter. Our count will be too high, so we will use division to reduce our count.

8. How many ways can Mary John and Susan be ordered? n = 3 X 2 X 1 = 6 1st2nd 3rd 321 We have counted the same case 6 times

9. To offset this, divide the number of permutations by 6 (6 / 6 = 1 case counted). (this allows us to keep our permutation/ factorial structure…) 6 (notice), happens to be 3!, where 3 is the length of the subset.

10. We are going to use our permutation formula with a slight adjustment in the denominator. This adjustment will reduce the total count by the correct amount.

11. Combination A combination is a collection of chosen objects for which order does not matter. C(n,r), nCr, or n, represent the number of combinations possible in which r objects are selected from a set of n different objects. r

12. Think of poker 52 P 5 = 52 C 5 = Recognize the difference

13. C(n,r) = n! (n – r)!r! The only difference between the permutation formula and the combination formula is the extra divisor of r!

14. How many different sampler dishes with 3 different flavours could you get at an ice cream shop with 31 different flavours? n = 31 and r = 3 C(31,3) = 31! (31 – 3)!3! = 4495

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