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Unformatted text preview: CS70: Satish Rao: Lecture 15. Outline. 1. Counting. 2. Enumerate 3. Tree 4. Rules of Counting 5. Sample with/without replacement where order does/doesnt matter. Probability is soon..but first lets count. Count? How many outcomes possible for k coin tosses? How many poker hands? How many handshakes for n people? How many diagonals in a convex polygon? How many 10 digit numbers? How many 10 digit numbers without repetition? Enumerate 000 Enumerate 000 1 (helan) 001 Enumerate 000 1 (helan) 001 2 (halvan) 010 Enumerate 000 1 (helan) 001 2 (halvan) 010 3 (tersen) 011 Enumerate 000 1 (helan) 001 2 (halvan) 010 3 (tersen) 011 4 100 Enumerate 000 1 (helan) 001 2 (halvan) 010 3 (tersen) 011 4 100 5 101 Enumerate 000 1 (helan) 001 2 (halvan) 010 3 (tersen) 011 4 100 5 101 6 110 Enumerate 000 1 (helan) 001 2 (halvan) 010 3 (tersen) 011 4 100 5 101 6 110 7 111 Enumerate 000 1 (helan) 001 2 (halvan) 010 3 (tersen) 011 4 100 5 101 6 110 7 111 8 Using a tree.. 000 001 1 010 011 1 1 100 101 1 110 111 1 1 1 Using a tree.. 000 001 1 010 011 1 1 100 101 1 110 111 1 1 1 Using a tree.. 000 001 1 010 011 1 1 100 101 1 110 111 1 1 1 Using a tree.. 000 001 1 010 011 1 1 100 101 1 110 111 1 1 1 Using a tree.. 000 001 1 010 011 1 1 100 101 1 110 111 1 1 1 8 leaves which is 2 2 2 . First Rule of Counting: Product Rule Objects made by choosing from n 1 , then n 2 , ... , then n k the number of objects is n 1 n 2 n k . First Rule of Counting: Product Rule Objects made by choosing from n 1 , then n 2 , ... , then n k the number of objects is n 1 n 2 n k . n 1 First Rule of Counting: Product Rule Objects made by choosing from n 1 , then n 2 , ... , then n k the number of objects is n 1 n 2 n k . n 1 n 2 First Rule of Counting: Product Rule Objects made by choosing from n 1 , then n 2 , ... , then n k the number of objects is n 1 n 2 n k . n 1 n 2 n 3 First Rule of Counting: Product Rule Objects made by choosing from n 1 , then n 2 , ... , then n k the number of objects is n 1 n 2 n k . n 1 n 2 n 3 In picture, 2 2 3 = 12! First Rule of Counting: Product Rule Objects made by choosing from n 1 , then n 2 , ... , then n k the number of objects is n 1 n 2 n k . n 1 n 2 n 3 In picture, 2 2 3 = 12! Remember the first rule.....
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 Fall '11
 Rau

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