Explanation:
distinct ways !
STATICS and STATICS are 2 different ways to arrange them. have you noticed the difference ?
no, of course not. I only exchanged the 2 S. the same problem with the 2 T.
while they are different permutations, their arrangements are not distinctly different. to us observers they look the same.
so, for the 7 letters, 7! is not the full answer.
these 7! permutations include all the ones, where we only change the S and the T with each other.
we need to eliminate those. we do this by dividing by the S permutations (2! = 2) and the T permutations (again, 2! = 2).
so, the answer is
7! / (2×2) = 5040 / 4 = 1260
the 7 letters can be arranged in 1260 distinctly different ways.