Question

In 8 fair coin flips, how many possible ways can you get 5 heads in a row? (Including more than 5 in a row as well)

Answer 1

See a solution process below:

Explanation:

If there are 8 heads in a row from the coin flips - there is 1 way to get this.

1. H H H H H H H H

If there are 7 heads in a row from the coin flips - there are 2 ways to get this:

1, H H H H H H H T
2. T H H H H H H H

If there are 6 heads in a row from the coin flips - there are 3 ways to get this

1. H H H H H H T ?
2. T H H H H H H T
3. ? T H H H H H H

If there are 5 heads in a row from the coin flips - there are 4 ways to get this

1. H H H H H T ? ?
2. T H H H H H T ?
3. ? T H H H H H T
4. ? ? T H H H H H

The total number of ways to get 5 heads in a row is:

1 + 2 + 3 + 4 = 10