Question

Assume that X={E,G,B,C} and Y={7,3,6,5}. A code consists of 2 different symbols selected from X followed by 3 not necessarily different symbols from Y. How many different codes are possible?

Answer 1

The number of permutations of the four different letters taken two at a time, without repetitions is 4P2.
The number of permutations of the four different numbers taken three at a time, with repetitions is 4^3.
The total number of different codes that are possible is given by:
\[\large \frac{4\times3\times2\times1}{2}\times4^{3}=you\ can\ calculate\]