How many 5bit strings begin with 1 11 111 1111 or 11111Solut

How many 5-bit strings begin with 1, 11, 111. 1111 or 11111?

Solution

=> 5 bit string starting with 1 = 1_ _ _ _ = these empty four places can either take 0 or 1 , therefore can be filled in 2^4 ways = 16

=> 5 bit string starting with 11 = 1 1 _ _ _ = these empty three sapces can be either 0 or 1 , therefore can be filled in 2^3 ways = 8

=> 5 bit string starting with 111 = 1 1 1 _ _ = these empty two sapces can be either 0 or 1 , therefore can be filled in 2^2 ways = 4

=> 5 bit string starting with 11 = 1 1 1 1 _ = these empty sapce can be either 0 or 1 , therefore can be filled in 2

=> 5 bit string starting with 11111 = it is the only string which can be formed , therefore 1.