Find the number of all even 2-digit numbers t | vedclass

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(C) $2$-digit number is represented as $XY$,where $X$ is the tens digit and $Y$ is the units digit.For a number to be even,the units digit $Y$ must be

Vedclass · Accepted Answer

$36$

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(C) $2$-digit number is represented as $XY$,where $X$ is the tens digit and $Y$ is the units digit.For a number to be even,the units digit $Y$ must be from the set $\{0, 2, 4, 6, 8\}$.The problem states that the units digit cannot be $0$,so $Y \in \{2, 4, 6, 8\}$. There are $4$ possible choices for the units place.The tens digit $X$ can be any digit from $\{1, 2, 3, 4, 5, 6, 7, 8, 9\}$. Note that $0$ cannot be in the tens place for a $2$-digit number. There are $9$ possible choices for the tens place.Total number of such even $2$-digit numbers $= (	ext{Choices for tens place}) 	imes (	ext{Choices for units place}) = 9 	imes 4 = 36$.

Find the number of all even $2$-digit numbers that do not have $0$ at the unit's place.

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