How many different codes are possible?

Question

Assume that X = { G, C, D, B, E} and Y = { 6, 2, 5, 4, 3, 7}. A code consists of 3 different symbols selected from X followed by 4 not necessarily different symbols from Y.

Answer 1

from X you choose 3 different symbols...

first choice you choose from 5 symbols

second choice you choose from 4 symbols

third choice you choose from 3 symbols

5*4*3 so far !!

from Y you choose 4 symbols with repetition...

first choice you choose from 6 symbols

second choice you choose from 6 symbols

third choice you choose from 6 symbols

fourth choice you choose from 6 symbols

6*6*6*6

answer: 5*4*3*6*6*6*6=77,760 different codes