  In this thesis we develop FPTASs for the counting problems of m-tuples,
contingency tables with two rows, and 0/1 knapsack. For the problem of counting
m-tuples, we design two algorithms, one is strongly polynomial. As far as we
know, these are the first FPTASs for this problem. For the problem of counting
contingency tables we improve significantly over the running time of existing
algorithms. For the problem of counting 0/1 knapsack solutions, we design a
simple strongly polynomial algorithm, with similar running times to the
existing algorithms. Our results are derived by using, as well as expanding,
the method of K-approximation sets and functions.
