For another example, consider the diagram formed by joining all the half-lines of one X to all the half-lines of another X. This diagram is called a vacuum bubble, because it does not link up to any external lines. There are 4! ways to form this diagram, but the denominator includes a 2! (from the expansion of the exponential, there are two X s) and two factors of 4!. The contribution is multiplied by ⁠ 4! / 2 × 4! × 4! ⁠ = ⁠ 1 / 48 ⁠.