Nevermind on this. I figured out that you have to arrange all the numbers of 1, 2, 3 in different order and find how many ascents there are to each.
A bit confused on how to begin this.
Consider the permutation of 1, 2, 3, 4. The permutation 1432, for instance, is said to have one ascent – namely, 14 (since 1 < 4). This same permutation also has two descents – namely, 43 (since 4 > 3) and 32 (since 3 > 2). The permutation 1423, on the other hand, has two ascents, at 14 and 23 – and the one descent 42.
a) How many permutations of 1, 2, 3 have k ascents, for k = 0, 1, 2?