Answer: So our limit is 1 million attempts.
a) 6 lower case letters.
Think in 6 blank spaces where you can put one letter, so in each space you have 26 options, so the total of combinations is = 308915776.
so if you have 1 million attempts, then 1000000/308915776 = 0.00323
so you have 0.32% chances of breaking the code.
b) 6 different letters, some may be upper-case, and it is case-sensitive
Again 6 blank spaces, in the first you can put 26 letters, and because its case sensitive, you have 52 options, in the second space, you will have 25 posible letters, and 50 options, and so on.
So the total combinations are 52*50*48*46*44*42 = 10608998400
and the probability of breaking it with 1 mill attempts is = 0.009%
(c) any 6 letters, upper- or lower-case, and it is case-sensitive
same as the first case, but here you have 26 lower case and 26 upper, so you have = 19770609664 combinations
and in 1 mill attempts the probability of breaking it is 0.0005%
(d) any 6 characters including letters and digits
Here you have 26 letters and 10 numbers, so the total combinations are :
= 2176782336
and the probability of breaking it will be 0.004%
were in all cases you must think that each attempt made by the spyware is a different combination, so the one million tries are different combinations.