How many even numbers of 3 different digits c | vedclass

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(A) number is even if its unit digit is even. The available digits are ${1, 2, 3, 4, 5, 6, 7, 8, 9}$.The even digits available are ${2, 4, 6, 8}$.Step

Vedclass · Accepted Answer

$224$

Vedclass · Answer

(A) number is even if its unit digit is even. The available digits are ${1, 2, 3, 4, 5, 6, 7, 8, 9}$.The even digits available are ${2, 4, 6, 8}$.Step $1$: The unit digit can be filled in $4$ ways (choosing from $2, 4, 6, 8$).Step $2$: Since repetition is not allowed,we have $8$ remaining digits to fill the remaining $2$ places.Step $3$: The number of ways to arrange $2$ digits out of the remaining $8$ is given by $^8P_2 = 8 	imes 7 = 56$.Step $4$: Total even numbers $= 4 	imes 56 = 224$.

How many even numbers of $3$ different digits can be formed from the digits $1, 2, 3, 4, 5, 6, 7, 8, 9$ (repetition is not allowed)?

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