Why are kernel methods with RBFs effective for handwritten digits (letters) classification?

I'm trying to get a overall picture of support vector machines, and came across kernel functions in the descriptions K(x1, x2) Can someone provide an big picture explanation of how does the kernel function quantifies similarity in different scenarios...

-if repetition of digits is allowed, but repetition of letters is not allowed determine the number of different passwords that can be made. - if repetition is not allowed for digits or letters determine how many fewer different passwords can be made

With the increased bunch of data around, traditional kernel function based SVM learners or variants are not capable of process data with relatively low budget machines. Therefore people, ML guys devise some methods to project data explicitly to approximated...

Digits are from 0 to 9 How many license plates can New Jersey issue wwithout repeating any letters or digits

License plates are made using 3 letters followed by 3 digits how many can be made if repetition of letters and digits is allowed?

I was hoping someone could point me in the right direction to either create or locate a program (even hire), that I can enter the known digits and it will generate the last remaining digits. For example, if the code was 4G78-7891HX-XXXX I would want...

How do you do estimation when working on Kernel or driver development which involves study of kernel code identifying hooks / APIs and feasibility etc.