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  Counting Principles and Probability Adriell Afable 11 -Salvation  2 The Fundamental Counting Principle states that if one event can occur m ways and a second event can occur n ways, the number of ways the two events can occur in sequence is m ã n . 1 st Coin Tossed Start HeadsTailsHeadsTails 2 nd Coin Tossed There are 2   2 different outcomes: {HH, HT, TH, TT}. HeadsTails 2 ways to flip the coin. 2 ways to flip the coin.  3 Example : A meal consists of a main dish, a side dish, and a dessert. How many different meals can  be selected if there are 4 main dishes, 2 side dishes and 5 desserts available? # of main dishes# of side dishes# of desserts 452   =There are 40 meals available. 40  4 A permutation is an ordered  arrangement of n different elements. How many permutations are possible using the three colors red, white, and blue?There are 3 choices for the first color, 2 choices for the second color and only 1 choice for the third color. 3! = 3 ã 2 ã 1 = 6 permutations “factorial”
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