The sum of the four-digit even numbers that c | vedclass

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(B) To form a four-digit even number using the digits $0, 3, 5, 4$ without repetition,the last digit must be $0$ or $4$.Case $1$: The last digit is $0

Vedclass · Accepted Answer

$43536$

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(B) To form a four-digit even number using the digits $0, 3, 5, 4$ without repetition,the last digit must be $0$ or $4$.Case $1$: The last digit is $0$. The remaining $3$ positions can be filled by $3, 5, 4$ in $3! = 6$ ways. The numbers are $3540, 5340, 3450, 4350, 5430, 4530$. Their sum is $3540 + 5340 + 3450 + 4350 + 5430 + 4530 = 26640$.Case $2$: The last digit is $4$. The first digit cannot be $0$. The possible numbers are $3054, 3504, 5034, 5304$. Their sum is $3054 + 3504 + 5034 + 5304 = 16896$.Total sum $= 26640 + 16896 = 43536$.

The sum of the four-digit even numbers that can be formed with the digits $0, 3, 5, 4$ without repetition is:

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