Thread: 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 .