Question

how many 3 digit even numbers can be made using the digits 1 ,2, 3, 4 ,6 ,7 of no digit is repeated?

Answer 1

The 3 digit even number has to end in 2, 4 or 6. Let us consider the cases separately
Ending in 2: 1st digit can be any of 5 from 1,3,4,6,7 and 2nd digit can be any of 4 remaining digits.
Hence number of possibilities = 5*4 = 20
Exactly the same logic yields number of numbers ending in 4 = 20 and nuber of numbers ending in 6 = 20
Hence total number of 3 digit even numbers = 20+20+20 = 60
Answer: 60