There are ten possible numbers, 26 possible Uppercase letters, and 26 possible lowercase letters. 10*26*26=6760. divide that by the total combinations to get the number of special characters: 223,080/6760
if you know the numbers and uppercase that takes the 10*26 out of the equation leaving 26*33= 858
divide 858 by 223,030 and simplify
I couldn't get the picture of the work on the train question, but:
the engine can not be arranged but the 6 cars can be.
this is also a permutation since the order of the cars matters; if you have a car placed second you can't place another car second.
So with 6 cars with 6 places it can go:
6*5*4*3*2*1 = 720 different arrangements