How many bit strings of length 7 begin with four 0's?

Question

If a bit string of length 7 begins with four 0's, then _____ positions remain to be filled in. Since each of these positions can be filled with either a 0 or a 1, the number of bit string of length 7 that begin with four 0's is _____.

Answer 1

If a bit string of length 7 begins with four 0's, then 3 positions remain to be filled in.

SInce each of these position can be filled with either a 0 or a 1, the number of bit

string of length 7 that begin with four 0's is 2*2*2 = 8