
Permutations
What is the total number of ways in which six 't' signs and four 't' signs can be arranged in a line such that no two '' signs occur together?
I have come up with possble orderings of:
t  t  t  t t  t  : having 2 t's together
t t t  t  t  t  : having 3 t's together
The answer is 35.
I come up with 3!4! + 4!4! from the above method so I must be doing something very wrong

There are 7 places between t's and at both ends. Each place can accommodate at most one . Therefore, the answer is $\displaystyle {7\choose 4}$.