How many different possible arrangements S can be obtained from the letters G, M, A, T, I, I, and T, such that there is at least one character between both I's? Choose the correct choice from the following answers.
A) 360
B) 720
C) 900
D) 1800
E) 5040
Total ways for arranging without restriction = 7!/ (2!2!) { 2! is becoz of two T's and other 2! for two I's)   Restriction : atleast one character between I's = Possible ways - both I's together i.e.o character between I's   _ _ _ _ _ (I I)   Both I's Together = 6! (Assuming 2 I's as one unit) /2!(for 2 T's) * 2! (No of arrangements of 2 I's)/2! (for 2 I's)   =6!/2!   Therefore ans S= 7!/ (2!2!) -6!/2! = 900   HEN900E 900.
<result>C</result>
How many different possible arrangements S can be obtained from the letters G, M, A, T, I, I, and T, such that there is at least one character between both I's?