The number of five-digit numbers divisible by | vedclass

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Question

(B) five-digit number is divisible by $5$ if its unit place is either $0$ or $5$. Case $I$: When $0$ is in the unit place,the remaining $4$ positions

Vedclass · Accepted Answer

$216$

Vedclass · Answer

(B) five-digit number is divisible by $5$ if its unit place is either $0$ or $5$. Case $I$: When $0$ is in the unit place,the remaining $4$ positions can be filled by the remaining $5$ digits $(1, 2, 3, 4, 5)$ in $^5P_4 = 120$ ways. Case $II$: When $5$ is in the unit place,the first position (ten-thousands place) cannot be $0$. Thus,the first position can be filled by any of the $4$ digits $(1, 2, 3, 4)$. The remaining $3$ positions can be filled by the remaining $4$ digits (including $0$) in $^4P_3$ ways. Number of ways for Case $II = 4 	imes ^4P_3 = 4 	imes 24 = 96$. Total number of ways $= 120 + 96 = 216$.

The number of five-digit numbers divisible by $5$ that can be formed using the digits $0, 1, 2, 3, 4, 5$ without repetition is

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