How many $5$ digit numbers can be formed using the digits $1, 2, 3, 4, 5, 6, 7, 8, 9$ such that no two consecutive digits are the same?

none of these

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9 \times 8^{4}

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9^{5}

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8^{5}

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Solution

The correct option is D $9 \times 8^{4}$
$5$ digit numberd
$1, 2, 3, 4, 5, 6, 7, 8, 9$
Total number of possible numbers
$\Rightarrow 9 \times 8 \times 8 \times 8 \times 8 \Rightarrow 9 \times (8)^{4}$

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