Question

Number of bit strings of length 5 with two or more consecutive zeros is______.

• A. 12
• B. 16
• C. 19
• D. 17

Answer 1

The correct option is C 19

option (a)

Number of bit srings of length
$5=2^5=32$

Indirect counting:

Let us enumerate number of invalid strings.

Case 1: Number of bit strings with no zeros = 1

Case 2 : Number of bit strings with one zero
$={}^5{C}_1=5$

Case 3: Number of bits strings with two separated zeros
$={}^4{C}_2=6$

Case 4 : Number of bit strings with three separated zeros
${}^3{C}_3=1$

$\therefore$ Required number of strings
$=32-(1+5+6+1)$

= 19