How many different codes are possible?

Question

Assume that X={A, G, F, B, C} and Y={5,3,7}. A code consists of 3 different symbols selected from X followed by 3 not necessarily different symbols from Y

Answer 1

Using the counting principle the number of possible codes from set X times the number of possible codes from set Y should give you the total number of codes. The permutations from set X come from the permutations formula (I'm assuming order matters)

P(5,3) = 5!/(5-3)! = 60

The combinations from set Y come from the counting principle

3³=27

The total number of codes is then 60×27 = 1620