Why do we need to divide by 2! while considering the combinations in Enigma machine? I would like to know why do we need to divide by 2! while considering pairs in p.11 of Enigma Machine.The article says that: "Number of ways to choose four letters from 26 letters is $\frac {{26 \choose 4}{4 \choose 2}{2 \choose 2}}{2!}$" but I can't get why do we need to divide by 2! since I think we're all have already done all the divisions to consider the combinations of the letters in the Enigma Machine.

$\binom{24}{4}\binom 42\binom 22/2!$ counts selections of 4 from 24 letters (without replacement) into two pairs when we consider permutation _of the pairs_ to be indistinct.

That is: we could select, for instance, ABCD, then divide them into pairs in three ways; which is $\binom 42/2!$ because, those pairings on the left column of the table are indistinct from those on the right of the same row. $$\begin{array}{c:c}AB,CD & CD, AB\\\ \hdashline AC,BD & BD,AC\\\ \hdashline AD, BC& BC, AD\\\ \end{array}$$