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Que. The number of bit strings of length eight that will either start with a 1 bit or end with two bits 00 shall be
a. 32
b. 64
c. 128
d. 160
Answer:32
Savita :(May 11, 2018) Answer of this question will be 160 plz update
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Savita :(May 11, 2018) Answer of this question will be 160 plz update
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Biswajit :(June 14, 2018) This comes under Discrete Mathematics

We need to follow the subtraction rule |AUB| = |A| + |B| - |A intersect B|

A => Start with 1; 1 place is fixed, therefore (8-1) = 7; 7 places can take two choices 0 and 1, so 2^7 = 128

B => Ends with 00; 2 places is fixed, therefore (8-2) = 6; 6 places can take two choices 0 and 1, so 2^6 = 64

|A intersect B| => Start with 1; and end with 00; 3 places is fixed, therefore (8-3) = 5; 5 places can take two choices 0 and 1, so 2^5 = 32

As per subtraction rule A and B are not disjoint sets so the intersection part needs to be subtracted.

which is 128+64-32 = 160, the answer.

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