CMPE 16 Winter 2016 Quiz9
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1. (2 points) What is the probability of being dealt a 5 card flush (5 cards of the same
suit) in poker? Show your work, but no need to do the arithmetic.
2. (4 points) Towers of Hanoi: Given that Hn = 2Hn1 + 1 and that T1 = 1, prove that
Hn = 2n 1.
Induc
1. (3 points) Use the principle of inculusion—exclusion to ﬁnd the number of positive
integers less than 1,000,000 that are not divisible by either 6 or 9.
Principle of inclusionexclusion (1 point):
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1. (2 points) Show that E E 2 1. If you can’t do that, for 1 point, show that
1% é=kn+1 I; 4"“ J
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2. (4 points) Prove that VnElkn E the natural numbers, Z"
1. (4 points) Give a formal proof of this statement: [(39 —> (1) /\ (119 —> q)] —> q.
List your steps and the justiﬁcation for each step.
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