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