Basic discrete combinatorics questions I have problems with We just started learning counting and I'm very confused. Every question I get is met with a lot of thinking and I still don't get "it". Can I get some help with the following question?
A password consists only small letters a,…,z
a. How many different passwords of sizes greater than 17 and lower than 20 are there?
My answer - This one is easy enough. The alphabet is 26 so the amount is $26^{18}$ * $26^{19}$ = $26^{37}$
b. How many passwords of length 8 in which there are at least two different consecutive letters are there?
My answer - I believe this one is all of the possibilities except the 26 possibilities of 8 times a, 8 times b, etc... $26^8-26$
c. How many passwords are there of length 8 in which after a letter appears it cannot be written again in the next two places after it (meaning: a letter cannot repeat consecutively, and cannot repeat after skipping just one letter)?
My answer - pretty sure about this one. $26*25*24^6 $
d. How many possibilities are there to put in a hat two identical folded notes such that on
one of them is a password of length 6 and on the other a password of length 7, such that no letter repeats twice (not on the same note, and not between the two notes)? Is
the answer different when the notes are of different colors? Explain.
My answer - This is where I have a lot of confusion. I eventually came to the conclusion that the answer is not different when the notes are of different colors. The number I got is $8 *10 *37! = 80*37!$ 
e. How many possibilities are there to put in a hat two identical folded notes such that on
one of them is a password of length 14 and on the other a password of length 15, such
that no letter repeats twice (not on the same note, and not between the two notes)?
No idea what to do here. help?
f. How many possibilities are there to put in a hat two identical folded notes such that on
each of them is a password of length 6, and no letter appears twice (not on the same
note, and not between the two notes)? Is the answer different when the notes are of
different colors? Explain.
No idea what to do here. help?
g. How many possibilities are there to put in a hat two identical folded notes such that on
each of them is a password of length 6? Is the answer different when the notes are of
different colors? Explain.
No idea what to do here. help?
 A: a. As mentioned by @Unwisdom, you should sum the number of possible passwords of length 18 and 19, rather than multiply them.
b. This is phrased somewhat poorly, but your interpretation seems correct.
c. Your answer is correct.
d. You have 26 total letters, and will be using 13 of them. How many ways can you choose this? Next, consider how many ways you can arrange these 13 letters, and a procedure for constructing a 6-letter password and a 7-letter password. See the comment made by @JMoravitz for elaboration on the second part. As for the colors, you are correct in saying the answer doesn't change, as the passwords are of two different lengths.
e. You have 26 letters, and need to choose 29 distinct letters to create your two passwords. Is this possible?
f. See a comment made by @JMoravitz for this.
g. Note that now, you can repeat letters. When creating each password of length 6, you have 26 options per letter. Therefore, there are $26^6$ options for password 1, and $26^6$ options for password 2. As the passwords are the same length, coloring them will increase the count.
