1.The integer 388,800 can be factored with primes as 2^6 × 3^5 × 5^2 (a) How many unique divisors does 388,800 have? (b) How many of these factors are even? odd? I have no clue how to do this. There are no similar examples in our textbooks or notes. I searched up counting divisors on the internet and couldn't understand it very well. Help? 2.The letters a, b, c, d, e, f, g can be arranged to form a number of words or sequences of up to length 7 [no repeated letters are allowed]. (a) Let S be the set of all words of length 7. What is n(S)? (b) Let X be the set of all words of length 6. What is n(X)? (c) Let U be the set of all words from length 1 to length 7. What is n(U)? (d) How many words in U do not begin with a? Do I solve a) and b) with permutations? Why is it that both of them yield the same answer? n(S) = 7!/0 = 7! n(X) = 7!/ (7-6)! = 7! What would I do for c) and d)? 3. A and B are sets where n(U) = 500, n(A) = 223, n(B) = 333, and n(A()B) = 133. Determine: (a) n(A()B′), () = the intersection of If I know n(A) = 223 and n(B') = 500-333=167, it doesn't seem plausible to find how many elements are in both (but I know there is a way!).