1. How many permutations of ALGORITHM have the A, L, and 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 I's? b. How many bytes contain at least one 1? c. How many bytes end with three I's or begin with two O's? d. How many bytes contain at least three 1's and at least two O's? 3. For n > 0, consider strings of length 2n of O's and 1's. Assuming all such strings are equally likely, what is the probability that one such 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