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GATE Overflow Test Series | Discrete Mathematics | Test 2 | Question: 3

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Total number of binary string of length $10$ is  $2^{10} =1024$ as each position has $2$ options - $0$ or $1.$

Number of binary string of length $10$ and ending with $111 = 2^7 = 128$ (last $3$ positions being fixed)

$\therefore$ The number of binary string not ending with $111  = 1024-128 = 896.$
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