For (i), it's just arrange anyhow & order doesn't matter. For (ii), there's a 2 in front because either there are 2 options(2 of S). There's a 3 at the back because there are 3 options (1st T/2nd T/3rd T). There's a 7! since you're just arranging in the middle (without regard for order).For (iii), there's a 3 because there are 3 options for the first spot (A/A/I). There's 8! because you're arranging the remaining 8 numbers anyhow. For (iv), you're arranging all the other 7 letters anyhow so there's 7! . There are 8 slots to insert the 2 of S in (6 between the 7 letters and another 2 on the sides) so there's 8C2. Among the 2 slots chosen, for the first slot there are 2 options ( 1st S/2nd S) and for 2nd slot there's one option hence there's 2! . Same logic for (v)