How many ways can a coin come up heads seven times and tails once when tossed eight times?

If you toss a coin 8 times and there are 7 heads, then there must be one tail each time.

So how many ways can we get one tail?

It can occur first, such as THHHHHHH or second HTHHHHHH etc.

There are 8 places to put the T so there are 8 ways to have 7 heads and 1 tail.