How many 3-digit numbers can be formed by usi | vedclass

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(C) $3$-digit number has three places: the hundreds place,the tens place,and the units place.$1$. The hundreds place cannot be $0$ because a number st

Vedclass · Accepted Answer

$100$

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(C) $3$-digit number has three places: the hundreds place,the tens place,and the units place.$1$. The hundreds place cannot be $0$ because a number starting with $0$ is not a $3$-digit number. The available digits are ${0, 2, 3, 6, 8}$. Excluding $0$,there are $4$ choices $(2, 3, 6, 8)$ for the hundreds place.$2$. Since repetition is allowed,the tens place can be filled by any of the $5$ digits $(0, 2, 3, 6, 8)$ in $5$ ways.$3$. Similarly,the units place can be filled by any of the $5$ digits in $5$ ways.Total number of $3$-digit numbers $= 4 	imes 5 	imes 5 = 100$.

How many $3$-digit numbers can be formed by using the digits $0, 2, 3, 6, 8$ when the digits may be repeated any number of times?

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