A pentomino is 5 squares joined edge-to-edge. There are exactly 12 distinct shapes. Together they cover 60 squares — and fit perfectly into a 6 × 10 rectangle, in 2,339 different ways.
Why 12?
Count carefully: shapes that are the same after flipping or rotating count as one. The 12 are usually labelled by the letters they look like — F, I, L, N, P, T, U, V, W, X, Y, Z.
Try the 5×12, 4×15, and 3×20 rectangles too. The 3×20 has only 2 solutions — much harder.