X={ F, G, E} and Y= {seven, six, five}. A code consist of two different sample selected from X followed by three not necessarily different symbols from why. How many different codes are possible?

Answer 1

Let's say the first task is to pick the two letters from set X, without any repeat.

This can be done in 6 ways: FG, GF, FE, EF, GE, EG. Note the permutations of any 2 letters, since different orders would give different codes. (This could also be figured out on your graphing calculator by using the Permutation function:

3 [_nP_r] 2 [Enter] , since we are permuting without repeats 2 items from 3 total distinct elements, and that would give the result 6 .)

The next task would be to choose the "three not necessarily symbols from Y". This could give us such as "765", "767", "555". This could be done in 3 (the number of elements to choose from) raised to the 3rd power (the number of times to select). Then 3³ is 27. (Could use the exponentiation key on the calculator, 3 [x^y] 3 [Enter] .)

Finally, the total number of ways to do both tasks, in that order, would be 6 * 27 = 162 possible "codes".