How many numbers can be formed using the digi | vedclass

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(C) To find the total numbers greater than $3000$ using the digits ${0, 1, 2, 3, 4, 5}$ without repetition,we consider numbers with $4, 5,$ and $6$ di

Vedclass · Accepted Answer

$1380$

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(C) To find the total numbers greater than $3000$ using the digits ${0, 1, 2, 3, 4, 5}$ without repetition,we consider numbers with $4, 5,$ and $6$ digits.$1$. $4$-digit numbers greater than $3000$:The first digit can be $3, 4,$ or $5$ ($3$ choices).The remaining $3$ positions can be filled by the remaining $5$ digits in $^5P_3 = 5 	imes 4 	imes 3 = 60$ ways.Total $4$-digit numbers $= 3 	imes 60 = 180$.$2$. $5$-digit numbers:The first digit cannot be $0$ ($5$ choices: $1, 2, 3, 4, 5$).The remaining $4$ positions can be filled by the remaining $5$ digits in $^5P_4 = 5 	imes 4 	imes 3 	imes 2 = 120$ ways.Total $5$-digit numbers $= 5 	imes 120 = 600$.$3$. $6$-digit numbers:The first digit cannot be $0$ ($5$ choices: $1, 2, 3, 4, 5$).The remaining $5$ positions can be filled by the remaining $5$ digits in $5! = 120$ ways.Total $6$-digit numbers $= 5 	imes 120 = 600$.Total numbers $= 180 + 600 + 600 = 1380$.

How many numbers can be formed using the digits $0, 1, 2, 3, 4, 5$ that are greater than $3000$ (repetition is not allowed)?

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