WRONG
There is a number of possible solutions that we can discuss.

RIGHT
There are a number of possible solutions that we can discuss.

WRONG
A number of protesters was seen outside the premises.

RIGHT
A number of protesters were seen outside the premises.

The phrase “a number of” is always followed by a plural verb, NOT a singular verb.

This is rather exceptional because “a number” is singular while the verb it goes with is in the plural. We do this because “a number of” means “several”, so refers to the plural. We use the plural verb to match the plural meaning of the phrase, NOT its singular grammar.