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(C) We need to find the number of four-digit numbers greater than $4321$ using digits $\{0, 1, 2, 3, 4, 5\}$.Case $1$: Numbers starting with $5$:The f

Vedclass · Accepted Answer

$310$

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(C) We need to find the number of four-digit numbers greater than $4321$ using digits $\{0, 1, 2, 3, 4, 5\}$.Case $1$: Numbers starting with $5$:The first digit is $5$. The remaining $3$ positions can be filled by any of the $6$ digits $(0-5)$.Number of ways $= 1 	imes 6 	imes 6 	imes 6 = 216$.Case $2$: Numbers starting with $44$ or $45$:The first digit is $4$. The second digit is $4$ or $5$ ($2$ choices). The remaining $2$ positions can be filled by any of the $6$ digits.Number of ways $= 1 	imes 2 	imes 6 	imes 6 = 72$.Case $3$: Numbers starting with $43$:The first two digits are $43$. The third digit must be greater than $2$,so it can be $3, 4, 5$ ($3$ choices).The fourth digit can be any of the $6$ digits.Number of ways $= 1 	imes 1 	imes 3 	imes 6 = 18$.Case $4$: Numbers starting with $432$:The first three digits are $432$. The fourth digit must be greater than $1$,so it can be $2, 3, 4, 5$ ($4$ choices).Number of ways $= 1 	imes 1 	imes 1 	imes 4 = 4$.Total count $= 216 + 72 + 18 + 4 = 310$.

The number of four-digit numbers strictly greater than $4321$ that can be formed using the digits $0, 1, 2, 3, 4, 5$ (repetition of digits is allowed) is

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