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

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Question

(A) To form a $3$-digit even number,the units place must be filled by an even digit from the given set $\{1, 2, 3, 4, 5, 6\}$.The even digits availabl

Vedclass · Accepted Answer

$108$

Vedclass · Answer

(A) To form a $3$-digit even number,the units place must be filled by an even digit from the given set $\{1, 2, 3, 4, 5, 6\}$.The even digits available are $2, 4, 6$. Thus,the units place can be filled in $3$ ways.Since repetition is allowed,the tens place can be filled by any of the $6$ digits in $6$ ways.Similarly,the hundreds place can be filled by any of the $6$ digits in $6$ ways.By the multiplication principle,the total number of $3$-digit even numbers is $6 	imes 6 	imes 3 = 108$.

How many $3$-digit even numbers can be formed from the digits $1, 2, 3, 4, 5, 6$ if the digits can be repeated?

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