Its given exactly 4 zero it means we have 6 1's which can be arranged in any order therefore 1! (since all 1 are identical)
1 1 1 1 1 1 since no two 0 should be consecutive we have total 7 space between each 1 we can place one 0
so select 7 places for 4 0's(all 0 are identical so we use the combination rather than permutation for arrangement) = 7C4
Therefore total binary string = 1! *7C4 =35