MATH1081 > 4 - Counting and Enumeration

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• A sequence of numbers a_n are defined by a_0=1, a_1=3, a_2=4
• Binary string, no triple zero
• Binary strings, no consecutive 1
• Counting
• Determine the particular solution
• Examples
• For nЄ1 consider the set of all n-digit numbers formed by the digits 1,2,3,4,5,6,7
• General Formula
• Given that the general solution of the homogeneous recurrence relation a_n−a_(n−1)−6_(n−2)=0 is hn=A(−2)^n+B(3)^n…
• How many 10 letter words …
• How many thirteen-card hands chosen from a standard pack contain
• Identifying Recursion
• Inclusion _ Exclusion Formula
• Non Homogeneous Solution
• Pigeonhole Principle
• Principles _ Rules
• Recursion
• Solve the recurrence a_n+5a_(n−1)−6a_(n−2)=(−6)^n
• Solve the recurrence a_n−a_(n−1)−6a_(n−2)=12
• Solve the recurrence relation a_n=2a_(n−1)+3a_(n−2) with initial conditions a_0=0 and a_1=4
• Solve the recurrence relation a_n=6a_(n−1)−9a_(n−2) with initial conditions a_0=4 and a_1=11
• Solve the recurrence relation a_n=−4a_(n−1)−4a_(n−2) with initial conditions a_0=3, and a_1=−2
• Solve the recurrence relation a_n=−5a_(n−1)−6a_(n−2) with initial conditions a_0=2 and a_1=1
• Straight lines are drawn on a piece of paper so that every pair of lines intersect but no three lines intersect at a common point
• Subtraction Rule
• Suppose that S is a set with n elements and T is a set with m elements
• Suppose that a person deposits $10000 in a savings account at a bank, yielding 5% per year with interest compounding annually
• Tower of Hanoi
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