In how many ways can 7 plus (+) and 5 minus (-) signs be arranged in a row so that no two minus (-) signs are together?

Explanation

In this method, first arrange the plus (+) signs.
Here, minus (-)signs=5
0+0+0+0+0+0+0+0
We can put minus (-) signn in any of the 8 places in the above arrangement i.e., we have to select 5 places out of 8 which can be done is `.^(8)C_(5)` ways=`.^(8)C_(3)` ways=56 ways.