how many 12bit strings begin with 0101 end with 110 and have

how many 12-bit strings begin with 0101, end with 110 and have 0010 as the four middle

Solution

a)out of 12 bits the first 4 bits are already given hence there are 8 bits to be filled each bit is having two chances either 0 or 1 so total no of possibilities is 2^8

b)out of 12 bits the end 3 bits are already given hence there are 9 bits to be filled each bit is having two chances either 0 or 1 so total no of possibilities is 2^9

c)similarly as already four bits arre choosen as earlier answer is 2^8