Example 1

P(5,2) = 20 — arrange 2 from 5

Example 2

C(6,2) = 15 — choose 2 from 6

Example 3

C(10,3) = 120 — choose 3 from 10

Example 4

P(4,4) = 24 = 4! — all arrangements

Example 5

C(8,5) = C(8,3) = 56 — symmetry