On all problems on this homework, feel free to leave answers in terms like "15 choose 4", no need to convert them to an actual number.

a. How many different strings can be formed by rearranging the letters in SARSAPARILLA?

b. What is the coefficient of w^(2) x^(7) z^(5) in (w + x + y + z)^(14)?

c. How many integers between 1 and 50 cant be divided by 3, 5, or 7?

d. How many 7-letter passwords are there that dont start or end with a Q? (as in class, assume passwords only consist of capital letters)

e. How many possible subsets of even size are there of a set with six elements?

f. How many 5-card poker hands can be made that only include spades and/or aces?

g. How many 8-letter passwords can be made where each letter is different than the letter before it? (so ABA would be okay but not AAB)