Hello Please help on thus question from Discrete Math. I solved the problem but want to make sure I have done it correctly. Thank you

1. This question is about passwords. In parts (a), (b), and (c), assume passwords are 10 characters long, and each character is either a lower case letter, upper case letter, or digit 0, . . . , 9

(a) How many possible passwords are there? A sophisticated password-guessing cluster2 can try 350 billion passwords per second. How many days will it take the cluster to try all of the passwords?

(b) How many passwords are there with at least one upper case letter, and also never repeat a character?

(c) How many passwords are the same written forwards and backwards?

(d) Now suppose we change the way passwords are selected. We take a dictionary containing 7776 words , and form a password by choosing 6 words (with repetition) and concatenating them (with spaces). So, for example, astor melee itch envoy larry ford is a possible password. (Note how easy it is to memorize such a password!)

Now how many possible passwords are there? How many days will it take the cluster from part (a) to try all possible passwords now?