Math Problem Statement
A binary string comprises 0’s and 1’s only. We consider all 8-bit binary strings, each of which contains exactly five 0’s and three 1’s. For example, 11100000 is a valid string whereas 10101110 is not. What is the number of such strings? Explain the counting argument you have used.
Solution
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Math Problem Analysis
Mathematical Concepts
Combinatorics
Binary Strings
Binomial Coefficients
Formulas
\( \binom{n}{k} = \frac{n!}{k!(n-k)!} \)
Theorems
Combination Formula
Suitable Grade Level
Grades 10-12