A bit string is a finite sequence of 0s and 1s How many bit

A bit string is a finite sequence of 0\'s and 1\'s. How many bit strings of length 8? How many bit strings of length 8 begin with three 0\'s? What is the probability a bit string of length 8 begins and ends with a 1?

Solution

Bit strings of length 8 are 28 i.e. 256 Strings starting with 3 0\'s i.e. 000xxxxx. therefore 3 positions are fixed and remaining are 5==>25 =32 strings starting with 0\'s. Strings starting and ending with 1 are 1xxxxxx1. therefore 2 positions are fixed and remaining are 6==>26 = 64 strings styarting and ending with 1. probability =64/256=0.25.