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Midterm #2 answers (questions have been paraphrased)
1. What's the probability of getting a straight dealt in order?
A. The first card can be a 2, 3, .
.., 10. That's 9 possibilities. Then each of the five cards can be any suit (but
we know what the ranks must be). That's another factor of 4^5. Then we divide by the number of ways of
being dealt 5 cards, which is 52 * 51 * 50 * 49 * 48.
2. How many strings with k 1s, no 000, and beginning and ending with 0?
A. Put in the k 1s first. Now put in 0s. At the beginning you could have either "0" or "00" before the first 1,
likewise at the end, so that's 2*2 choices. Then in between each pairs of 1s (and there are k1 such gaps) you
can have "00", "0", or "". That's 3^(k1) choices. So the total is 4 * 3^(k1).
3a. What's the biggest a_n could be in a slowgrowing sequence?
A. Well, a_n is bounded by a_(n1) + n, which is bounded by a_(n2) + (n1) + n, .
.., which is bounded by 1
+ 2 + .
.. + n. That's an okay answer, though summing it and getting [n+1 choose 2] is much nicer.
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 Spring '08
 STRAIN
 Probability

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