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

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Question

(C) To form a $3$-digit even number,the units place must be filled with an even digit from the set $\{1, 2, 3, 4, 6, 7\}$.The available even digits ar

Vedclass · Accepted Answer

$60$

Vedclass · Answer

(C) To form a $3$-digit even number,the units place must be filled with an even digit from the set $\{1, 2, 3, 4, 6, 7\}$.The available even digits are $2, 4,$ and $6$. Thus,the units place can be filled in $3$ ways.Since digits cannot be repeated,after filling the units place,we have $5$ digits remaining to fill the hundreds and tens places.The number of ways to fill the hundreds and tens places using the remaining $5$ digits is given by the permutation formula $^5P_2$.$^5P_2 = \frac{5!}{(5-2)!} = \frac{5 	imes 4 	imes 3!}{3!} = 5 	imes 4 = 20$.By the multiplication principle,the total number of $3$-digit even numbers is $3 	imes 20 = 60$.

How many $3$-digit even numbers can be formed using the digits $1, 2, 3, 4, 6, 7$,if no digit is repeated?

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