How many distinct three-letter sequences with at least one “T” can be formed by using three of the six letters of TARGET? One such sequence is “T-R-T.”
+128408 Sequences with one T =
(TAR) (TAG) (TAE)
(TRG) (TRE)
(TGE)
And each of these can be arranged in 6 ways....so....6 * 6 = 36 (!)
Sequences with two T's =
(TTA) (TTR) (TTG) (TTE)
And each of these can be arranged in 3 ways ,,,,so 4 * 3 = 12 (2)
So...adding (1) and (2) we get 48 arrangements with at least one T
