The digits 4, 5, 6, 7, 8 are written in every | vedclass

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(C) Total number of $5$-digit numbers formed using the digits $\{4, 5, 6, 7, 8\}$ is $5! = 120$.We need to find the number of arrangements greater tha

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$90$

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(C) Total number of $5$-digit numbers formed using the digits $\{4, 5, 6, 7, 8\}$ is $5! = 120$.We need to find the number of arrangements greater than $56000$.Total arrangements = $120$.Numbers starting with $4$ are $4! = 24$.Numbers starting with $54$ are $3! = 6$.Numbers starting with $55$ are not possible as digits are distinct.Numbers less than or equal to $56000$ are those starting with $4$ (all $24$) and those starting with $54$ (all $6$).Numbers less than $56000$ = $24 + 6 = 30$.Numbers greater than $56000$ = $120 - 30 = 90$.

The digits $4, 5, 6, 7, 8$ are written in every possible order. The number of numbers greater than $56000$ is

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