Question

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

Answer 1

Finding $3$ digit even number from given digit with no repetition.
The given digits are $1,2,3,4,6,7$
even digits are $2,4,6$
For an even number, units place should be even
So, no.of ways to fill units place with $3$ even digits $={}^3{P}_1=3$
No.of different ways to fill remaining $2$ places with order $5$ digits $={}^5{P}_2=\frac{5!}{(5-2)!}=\frac{5\times 4\times 3!}{3!}=20$

$\therefore$ Number of $3$ digit even numbers $=3\times 20=60$.