Question 1205238
<br>
There are 5 different letters: 3 each of S and T, 2 of I, and 1 each of A and C.<br>
To choose 4 letters, we have the following different cases to consider:
(1) 3 of one letter and 1 of a different letter
(2) 2 each of two different letters
(3) 2 of one letter and 1 each of two other letters
(4) 4 different letters<br>
(1) 3 and 1.  We need to...
choose one of the two letters that occurs 3 times: C(2,1)=2
choose one of the other 4 letters: C(4,1)=4
arrange the 4 letters in any of {{{4!/((3!)(1!))=4}}} ways<br>
Number of arrangements: (2)(4)(4) = 32<br>
(2) 2 and 2.  We need to...
choose two of the three letters that occurs 2 or more times: C(3,2)=3
arrange the 4 letters in any of {{{4!/((2!)(2!))=6}}} ways<br>
Number of arrangements: (3)(6) = 18<br>
(3) 2, 1, and 1.  We need to...
choose one of the three letters that occurs 2 or more times: C(3,1)=3
choose two of the other 4 letters: C(4,2)=6
arrange the 4 letters in any of {{{4!/((2!)(1!)(1!))=12}}} ways<br>
Number of arrangements: (3)(6)(12) = 216<br>
(4) 1, 1, 1, and 1.  We need to...
choose any 4 of the 5 letters: C(5,4)=1
arrange the 4 letters in any of 4! = 24 ways<br>
Number of arrangements: (5)(24) = 120<br>
Total number of arrangements: 32+18+216+120 = 386<br>
ANSWER: 386<br>