The number of five-digit numbers divisible by | vedclass

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(B) five-digit number is divisible by $5$ if its unit digit is $0$ or $5$. Case $I$: When $0$ is in the unit place. The remaining $4$ places can be fi

Vedclass · Accepted Answer

$216$

Vedclass · Answer

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