The number of four-digit even numbers that ca | vedclass

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(B) four-digit number is even if its unit digit is $0$ or $2$. Since repetition is not allowed,we consider two cases:Case $1$: The unit digit is $0$.T

Vedclass · Accepted Answer

$10$

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(B) four-digit number is even if its unit digit is $0$ or $2$. Since repetition is not allowed,we consider two cases:Case $1$: The unit digit is $0$.The remaining $3$ positions can be filled by the remaining $3$ digits $(1, 2, 3)$ in $3! = 3 	imes 2 	imes 1 = 6$ ways.Case $2$: The unit digit is $2$.The thousands place cannot be $0$ or $2$. Thus,the thousands place can be filled by $1$ or $3$ ($2$ ways).The remaining $2$ positions can be filled by the remaining $2$ digits in $2! = 2$ ways.Total ways for Case $2 = 2 	imes 2 = 4$ ways.Total even numbers = $6 + 4 = 10$.

The number of four-digit even numbers that can be formed using the digits $0, 1, 2,$ and $3$ without repetition is:

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