How many 4-digit even numbers can be formed u | vedclass

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(C) To form an even number,the unit's place must be occupied by $0, 2, 4,$ or $6$. We divide this into two cases:Case $I$: Unit's place is $0$.The num

Vedclass · Accepted Answer

$420$

Vedclass · Answer

(C) To form an even number,the unit's place must be occupied by $0, 2, 4,$ or $6$. We divide this into two cases:Case $I$: Unit's place is $0$.The number of ways to fill the unit's place is $1$. The remaining $3$ places can be filled by the remaining $6$ digits $(1, 2, 3, 4, 5, 6)$ in $^6P_3 = 6 	imes 5 	imes 4 = 120$ ways.Case $II$: Unit's place is $2, 4,$ or $6$.The number of ways to fill the unit's place is $3$. The thousand's place cannot be $0$ and cannot be the digit used in the unit's place,so there are $7 - 2 = 5$ choices for the thousand's place. The remaining $2$ places can be filled by the remaining $5$ digits in $^5P_2 = 5 	imes 4 = 20$ ways.Total ways for Case $II = 3 	imes 5 	imes 20 = 300$.Total even numbers $= 120 + 300 = 420$.

How many $4$-digit even numbers can be formed using the digits $0, 1, 2, 3, 4, 5, 6$ without repetition?

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