Question
How many bit strings of length ten either start with a 1 bit or end with two bits 00?
The correct answer is
640
There are \(2^9\) strings starting with 1 and \(2^8\) ending with 00. Their intersection fixes three bits and has \(2^7\) strings. Inclusion–exclusion gives \(2^9+2^8-2^7=512+256-128=640\).
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Important Questions from Generating Functions - Teaching
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