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(A) The available digits are $S = \{0, 2, 3, 4, 7, 9\}$. The total number of digits is $6$.Since the numbers are $5$-digit numbers,the first digit can

Vedclass · Accepted Answer

$2997$

Vedclass · Answer

(A) The available digits are $S = \{0, 2, 3, 4, 7, 9\}$. The total number of digits is $6$.Since the numbers are $5$-digit numbers,the first digit cannot be $0$. The possible first digits are $\{2, 3, 4, 7, 9\}$.Numbers starting with $2$: $1 	imes 6 	imes 6 	imes 6 	imes 6 = 1296$.Numbers starting with $3$: $1 	imes 6 	imes 6 	imes 6 	imes 6 = 1296$.Numbers starting with $40$: $1 	imes 1 	imes 6 	imes 6 	imes 6 = 216$.Numbers starting with $420$: $1 	imes 1 	imes 1 	imes 6 	imes 6 = 36$.Numbers starting with $422$: $1 	imes 1 	imes 1 	imes 6 	imes 6 = 36$.Numbers starting with $423$: $1 	imes 1 	imes 1 	imes 6 	imes 6 = 36$.Numbers starting with $424$: $1 	imes 1 	imes 1 	imes 6 	imes 6 = 36$.Numbers starting with $427$: $1 	imes 1 	imes 1 	imes 6 	imes 6 = 36$.Numbers starting with $4290$: $1 	imes 1 	imes 1 	imes 1 	imes 6 = 6$.Now,we count the numbers starting with $4292$:$42920$ is the $1$st number.$42922$ is the $2$nd number.$42923$ is the $3$rd number.Total serial number = $1296 + 1296 + 216 + 36 + 36 + 36 + 36 + 36 + 6 + 3 = 2997$.

Let $5$-digit numbers be constructed using the digits $0, 2, 3, 4, 7, 9$ with repetition allowed,and are arranged in ascending order with serial numbers. Then the serial number of the number $42923$ is $...............$.

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