Permutative ninja turtles

The latest xkcd got me thinking about how I've long liked the fact that the words in the "Teenage Mutant Ninja Turtles" theme can be easily permuted with no change to the rhythm of the song; for example, "Mutant Teenage Turtle Ninjas", and how changing the order of the words in this way makes repeating that line over and over a little more interesting, and while I love the thought of singing "William Henry, Duke of Gloucester" to the tune of the TMNT theme, it doesn't permute very well.

Heroes in a Half Shell by mattcantdraw

However, when permuting the words in the original TMNT theme, you can't really put "Teenage" in the last spot because the noun form is "Teenager", which breaks the rhythm. Without resorting to something awful like "Teener", then, how many permutations of TMNT does that leave us?

Combinatorics doesn't come naturally to most of the human species, but this one is relatively easy.  With no restrictions, we would normally note that there are 4 possible choices for the first spot, then 3 for the second, 2 for the third, and 1 remaining choice for the last slot, so 4*3*2*1 = 4! = 24 permutations.  With the restriction that only 3 of the options are available to the last spot, then there are 3 for the first spot, 2 for the second, and 1 remaining choice for the third, so 3*2*1*3 = 3*3! = 18 permutations before you have to repeat yourself.  Yay counting!