Answer to Question #140820 in Discrete Mathematics for Mahesh Daulat Rayate

Question

How many bit strings of length 8 either start with 1 bit or end with 2 bits 0

Answer 1

$\text {let }A=\{1xxxxxxx\}\text{where }x\isin\{0,1\}$

$\vert{A}\vert=2^7=128$

$\text {let }B=\{xxxxxx00\}\text{where }x\isin\{0,1\}$

$\vert{B}\vert=2^6=64$

$A\cap{}B=\{1xxxxx00\}\text{where }x\isin\{0,1\}$

$\vert{A\cap{}B}\vert=2^5=32$

$\text{according to Inclusion-exclusion principle }\vert{A\cup{}B}\vert=\vert{A}\vert+\vert{B}\vert-\vert{A\cap{}B}\vert$

$\vert{A\cup{}B}\vert=128+64-32=160$

Answer: 160