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The number of bit strings of length $8$ that will either start with $1$ or end with $00$ is?

  1. $32$              
  2. $128$             
  3. $160$          
  4. $192$
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string starting with 1 - 8 places 1 place fixed .7 places have 2 choices . 2^7=128

ending with 00- 8 places 2 fixed. =2^6=64

common strings will be there that have been counted twice are . starting with 1 and ending with 00. such number of string will be .

fix 3 position rest have 2 choices=32

total = 128+64-32=160
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