2015 NS 26

How did you get that?

All these are equivalent:
1 - 10 nPr 4 - 8 nPr 4             =3,360 
2 - [10 nPr 4]/2 + [8 nPr 4]/2 =3,360
3 - 9 nPr 4 =3,024 + 3024/9   =3,360

\(\text{There are 2 T's}\\ \text{So let's look at permutations by how many T's they contain}\\ 0 - \dbinom{4}{0}\dbinom{8}{4}4! = 1680\\ 1 - \dbinom{4}{1}\dbinom{8}{3}3! = 1344 \\ 2 -\dbinom{4}{2}\dbinom{8}{2}2! = 336\\ \text{These sum to }n = 3360\)

Thanks to all of you!!!