# lect2 - Last time we discussed The rule of sum The rule of...

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1 Last time we discussed: The rule of sum The rule of product Permutations = arrangements when the order is important a all objects are distinct/not all are distinct a without repetition/ with repetitions Combinations =selections when the order does not matter

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2 Suppose two dice are rolled, one blue and one red. How many outcomes are possible? How many outcomes are doubles? Product rule: 6 × 6=36 How many outcomes give the sum 7 or the sum 11? The rule of sum: 6 1+6 2+5 3+4 4+3 5+2 6+1 6 5+6 6+5 2
3 How many outcomes have the blue die showing 2? How many outcomes have exactly one die showing 2 ? How many outcomes have at least one die showing 2? How many outcomes have neither die showing 2? 6 5+5 10+1 5 × 5 36 - 11

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4 How many outcomes give an even sum? Possible even sums: 12, 10, 8, 6, 4, 2. 12=6+6 10=5+5 4+6 6+4 8=6+2 5+3 4+4 3+5 2+6 6=5+1 4+2 3+3 2+4 1+5 4=3+1 2+2 1+3 2=1+1
5 Suppose you have 12 students in the recitation class who are supposed to break up into 4 groups of 3 students each. How many different group assignments are possible?

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lect2 - Last time we discussed The rule of sum The rule of...

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