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."

Case 1: 1 T 

3 options for where the T is, 4 options for A, R, G or E and 3 for the last slot.

 

3 * 4 * 3 = 36

 

Case 2: 2 T's

3 options for non T's and four options for the last slot. 

 

3 * 4 =  12

 

Total:

 

36 + 12 = 48<------------Answer