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(1 point) [3 Marks] A 6-digit binary string a 6-digit number composed of Os and 1s. How many 6-digit binary strings have th

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\\ A: Set\ of\ strings\ with\ third\ digit\ as\ 0.\\ n(A): Number\ of\ strings\ with\ third\ digit\ as\ 0.\\ Fix\ the\ third\ digit\ as\ 0\\ \_ \ \_\ 0\ \_\ \_\ \_\\ Rest\ of\ 5\ digits\ can\ be\ either\ 0\ or\ 1.\\ Hence,\ n(A) = 2^5.\\ \\ B: Set\ of\ strings\ with\ 5th\ digit\ as\ 1.\\ n(B): Number\ of\ strings\ with\ 5th\ digit\ as\ 1.\\ Fix\ the\ 5th\ digit\ as\ 1\\ \_ \ \_\ \_\ \_\ 1\ \_\\ Rest\ of\ 5\ digits\ can\ be\ either\ 0\ or\ 1.\\ Hence,\ n(B) = 2^5.\\ \\ A\cap B: Set\ of\ strings\ with\ third\ digit\ as\ 0\ and\ 5th\ digit\ as\ 1.\\ n(A \cap B): Number\ of\ strings\ with\ third\ digit\ as\ 0\ and\ 5th\ digit\ as\ 1.\\ Fix\ the\ third\ digit\ as\ 0\ and\ 5th\ digit\ as\ 1.\\ \_ \ \_\ 0\ \_\ 1\ \_\\ Rest\ of\ 4\ digits\ can\ be\ either\ 0\ or\ 1.\\ Hence,\ number\ of\ such\ strings = 2^4.

\\ A\cup B: Set\ of\ strings\ with\ third\ digit\ as\ 0\ or\ 5th\ digit\ as\ 1.\\ n(A \cup B): Number\ of\ strings\ with\ third\ digit\ as\ 0\ or\ 5th\ digit\ as\ 1.\\ n(A \cup B) = n(A) + n(B) - n(A \cap B) = 2^5 + 2^5 - 2^4 = 2^6 - 2^4 = 48

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