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.
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '08
 STRAIN
 Probability, ternary strings, straight dealt, k1 such gaps, slowgrowing sequence, okay answer

Click to edit the document details