SDS321SampleFQ-1 - SDS321 Sample Questions for Final 1 How...

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SDS321 Sample Questions for Final 1. How many permutations of ALGORITHM have the A, L, and the G together in any order? 2. A byte consists of eight bits, each bit being a 0 or 1. a. How many bytes contain exactly three 1's? b. How many bytes contain at least one 1? c. How many bytes end with three 1's or begin with two 0’s? d. How many bytes contain at least three 1’s and at least two 0’s? 3. For n>0 , consider strings of length 2n of 0’s and 1’s. Assuming all such strings are equally likely, what is the probability that such a string has an equal number of 0’s and 1’s? 4. How many ways are there to choose a half dozen donuts from 10 varieties a. If there are no two donuts of the same variety. b. If there are at least two varieties. c. If there must be at least one but no more than 4 glazed. 5. Given a set A = {a,b,c,d,e}, A. How many different sequences of type A of length n>0 exist that contain at most one a? B. How many subsets of A are there? C. How many non-empty subsets of A are there? D. How many subsets of size 3 can you create from A? E. How many subsets of A are there that are entirely vowels or entirely consonants? F. How many subsets of A are there that have at least one vowel and one consonant?
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G. How many subsets of A of size 3 contain exactly one vowel. H. How many ways can you arrange the letters in A? I. How many ways can the letters of A be arranged so that all of the vowels are together? J. How many ways can you arrange the letters of A so that it is not the case that all of the vowels are together? K. How many ways can you arrange the letters in A so that vowels and consonants alternate and the arrangement begins with a consonant.
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