Another approach I thought is like :
Total number of arrangements : 8!/(2!*2!)
But these arrangements include orders like O → E → O , E → O → O , O → O → E. But we only want the first one instead of 3.
That is in place of 3 orders we want only 1. So divide 8!/(2!*2!) by 3. We get 3360.
More details :
Let x1,x2,x3,x4 be strings of letters comprising of different combinations of {T,T,S,B,K}.
For instance let x1=S,x2=B,x3=T,x4=KT. Then
x1 O x2 E x3 O x4
x1 E x2 O x3 O x4
x1 O x2 O x3 E x4
these are the arrangements we get out of which we want only one.
For each such x1,x2,x3,x4 we will get 3 orders and we want 1. So divide the whole no. of possible arrangement with 3.