I viewed Tony Sale's page to try to understand the math behind 150 million million permutations for the plugboard. His math was far too advanced for me, so I tried to approach it from a practical point of view.

With the first cord, I have 26 letters to choose from for one end, then (since a letter can't be plugged into itself) I have 25 letters to choose from for the other end. Since a letter can only be plugged into 1 other letter, that leaves 24 letters to choose from for the next cord.
Factoring 26 X 25 X 24 X ... X 7, my calculator showed the answer of approx. 5.6e23 or 56 thousand million million million, a number that's over 3.6 trillion times greater than the number that is reported in this article.

Is my calculator wrong or did Mr. Sale make a mistake? I genuinely would like to know, because I don't understand it.

This question is for testing whether you are a human visitor and to prevent automated spam submissions.