How many 3-digit even numbers can be made using the digits 1,2,3,4,5,6,7 if no digits is repeated?

Explanation

Total digits 1,2,3,4,6,7 = 6
`:.` Any number will be even when the 2,4 or 6 is unit place.
Then number of ways to write unit place.
`.^(3)P_(1) = (lfloor3)/(ul(3-1)) =(lfloor3)/(lfloor2) = (3xx2)/(lfloor2) = 3`
Now, number of ways to write ten,s and hundred's place.
`.^(5)P_(2) = (lfloor5)/(ul(5-2)) -(lfloor5)/(lfloor3) = (5 xx 4 xx lfloor3)/(lfloor3) = 5 xx 4 = 20`
Now, total three digit even numbers
`.^(5)P_(2) xx .^(3)P_(1) = 20 xx 3 = 60`