Represent k items as stars (*) and n-1 dividers as bars (|). Arrange them to distribute items into n types.
Example: choosing 5 items from 3 types. Use 5 stars and 2 bars: |*| means 2 of type 1, 1 of type 2, 2 of type 3.
Counting arrangements: you have 7 positions (5 stars + 2 bars), choose 2 for bars. C(7,2) = 21 ways.