How many numbers greater than 24,000 can be f | vedclass

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(C) We need to form $5$-digit numbers greater than $24,000$ using the digits ${1, 2, 3, 4, 5}$ without repetition.Case $1$: The first digit is $2$. To

Vedclass · Accepted Answer

$84$

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(C) We need to form $5$-digit numbers greater than $24,000$ using the digits ${1, 2, 3, 4, 5}$ without repetition.Case $1$: The first digit is $2$. To be greater than $24,000$,the second digit must be $4$ or $5$.- If the second digit is $4$,the remaining $3$ positions can be filled by the remaining $3$ digits in $3! = 6$ ways.- If the second digit is $5$,the remaining $3$ positions can be filled by the remaining $3$ digits in $3! = 6$ ways.Total for Case $1 = 6 + 6 = 12$ numbers.Case $2$: The first digit is $3, 4,$ or $5$ ($3$ choices).The remaining $4$ positions can be filled by the remaining $4$ digits in $4! = 24$ ways.Total for Case $2 = 3 	imes 24 = 72$ numbers.Total numbers $= 12 + 72 = 84$.

How many numbers greater than $24,000$ can be formed by using the digits $1, 2, 3, 4, 5$,when no digit is repeated?

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