Question

How many 5 digits numbers less than 60000 and even can be formed using the digits 1,2,4,5,7 and 9

Answer 1

This is tricky since we have over-lapping restrictions, so let's use cases
We can only use 1,2,4 or 5 at the front, (it has to be < 60000)

case1: it starts with 1 or 5
number of ways = 2*4*3*2*2 , the last 2 is for the 2 evens we can use
= 96
case2: it starts with a 2,
number of ways = 1*4*3*2*1 , the last can only be the 4
= 24
case3: it starts with a 4, which is the same as case2

number of ways = 96+24+24 = 144