How many different ways can 2 pounds be made by using 8 types coins such that: 1 pence, 2 pence, 5 pence, 10 pence, 20 pence, 50 pence, 1 pound, 2 pounds. Please use python code to fix this problem. And please provide algorithims code as many as you can, such like brute force, dynamic programing, recursion. We need to compare the algorithims and complexity.