Hello, I want to learn DM by myself, and asked a university prof. (different faculty) to give me a few exercises to solve.

Can You point me to subjects those are from and what should I learn as well as explain how those should be solved (with the solving itself done if possible)?

Use generating functions to find a_{n}if :a_{n}= a_{n - 1}+ 3n, for n >= 1

Find the number of ways to select 8 balls from the set of 5 identical red balls, 3 identical

yellow balls and 7 identical green balls.

Use the extended version of the Euclid's algorithm to compute EXT-EUCLID(24,42)

How many ways are there to distribute 18 balls among 6 different persons if

a) each ball is different and each person should get 3 balls

b) all balls are identical ?

How many permutations of the letters a, a, a, b, b, b, c, c, c, d, d, d, are there with no three

consecutive letters the same?

Show that P(n, k) = P(n - 1; k - 1) + P(n - k; k) for each 1 < k < n.