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(C) The total number of $5$-digit numbers formed using the digits $1, 2, 3, 4, 5$ is $5! = 120$.Numbers starting with $1$ are $4! = 24$.Numbers starti

Vedclass · Accepted Answer

$84$

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(C) The total number of $5$-digit numbers formed using the digits $1, 2, 3, 4, 5$ is $5! = 120$.Numbers starting with $1$ are $4! = 24$.Numbers starting with $21$ are $3! = 6$.Numbers starting with $23$ are $3! = 6$.Numbers starting with $24$ are $3! = 6$.Numbers starting with $25$ are $3! = 6$.Numbers starting with $3, 4, 5$ are $3 	imes 4! = 3 	imes 24 = 72$.Alternatively,we want numbers $> 24000$. Numbers starting with $1$ are $24$ (all $Numbers starting with $21$ are $6$ (all $Numbers starting with $23$ are $6$ (all $Total numbers less than or equal to $24000$ are $24 + 6 + 6 + 1 = 37$ (where $1$ is for the number $24000$ itself,but since we use digits $1-5$ only,$24000$ is not possible,so $24+6+6 = 36$).Total numbers greater than $24000$ are $120 - 36 = 84$.

How many numbers greater than $24000$ can be formed using the digits $1, 2, 3, 4, 5$ without repetition?

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