How many 3-digit even numbers can be formed u | vedclass

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(B) To form a $3$-digit even number,the unit's place must be occupied by an even digit ($0$ or $2$).Case $1$: Unit's place is $0$.The remaining two pl

Vedclass · Accepted Answer

$21$

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(B) To form a $3$-digit even number,the unit's place must be occupied by an even digit ($0$ or $2$).Case $1$: Unit's place is $0$.The remaining two places (hundreds and tens) can be filled by the remaining $4$ digits $(2, 3, 5, 7)$.The number of ways to fill the hundreds place is $4$ and the tens place is $3$.Total ways for Case $1 = 4 	imes 3 = 12$.Case $2$: Unit's place is $2$.The hundreds place cannot be $0$,and it cannot be $2$ (since repetition is not allowed).So,the hundreds place can be filled by any of the remaining $3$ digits $(3, 5, 7)$.The tens place can then be filled by any of the remaining $3$ digits (including $0$ but excluding the digits used in the hundreds and unit's places).Total ways for Case $2 = 3 	imes 3 = 9$.Total even numbers $= 12 + 9 = 21$.

How many $3$-digit even numbers can be formed using the digits $0, 2, 3, 5, 7$ when repetition is not allowed?

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