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(C) four-digit number is even if its unit digit is $0$ or $2$.Case $1$: The unit digit is $0$.The remaining $3$ positions can be filled by the remaini

Vedclass · Accepted Answer

$10$

Vedclass · Answer

(C) four-digit number is even if its unit digit is $0$ or $2$.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 $2$,so it can be filled in $2$ ways (using $1$ or $3$).The remaining $2$ positions can be filled by the remaining $2$ digits in $2! = 2 	imes 1 = 2$ ways.So,the number of ways is $2 	imes 2 = 4$ ways.Total even numbers $= 6 + 4 = 10$.

All possible four-digit numbers are formed using the digits $0, 1, 2, 3$ such that no digit is repeated. The number of even numbers among them is

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