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 ${4, 5, 6, 7, 8}$ without repetition is $5! = 120$.To find the numbers greater than $560

Vedclass · Accepted Answer

$90$

Vedclass · Answer

(C) Total number of $5$-digit numbers formed using the digits ${4, 5, 6, 7, 8}$ without repetition is $5! = 120$.To find the numbers greater than $56000$,we subtract the numbers less than or equal to $56000$ from the total.Numbers starting with $4$: There are $4! = 24$ such numbers.Numbers starting with $54$: There are $3! = 6$ such numbers.Numbers starting with $55$: Not possible as digits are distinct.Numbers starting with $56000$: Since the digits are ${4, 5, 6, 7, 8}$,the smallest number starting with $56$ is $56478$,which is already greater than $56000$.Thus,the numbers less than $56000$ are those starting with $4$ ($24$ numbers) and those starting with $54$ ($6$ numbers).Total numbers less than $56000 = 24 + 6 = 30$.Required 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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