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Counting and Combinations

Problem 1)
How many bits does 10^100 (ten power one hundred) have if written in base 2?

problem 2)
Find the number of all 20-digit integers in which NO two consecutive digits are the same

Please explain to me the steps, don't just give me the answer, thank you very much.

Solution Preview

Problem #1
To find the number of bits for 10^100, we only need to find log(2, 10^100), which means the logrithm of 10^100 with base 2. So log(2, 10^100) = ...

Solution Summary

Counting and combination problems are solved.

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