I assume that what you have mentioned as "bit" is binary numbers(am I correct?)

lets take one situation where there is three zero's

0,0,0,a,b,c,d,e

a,b,c,d and e can either be 1 or 0. So all possible combinations for arranging those would be .

just like the above situation there can be situations

so all possible combinations =

from this you can get the probability of getting a string containing exactly three 0's