Question

How many five digit numbers are there such that two left most digits are even and remaining are odd and digit 4 should not be repeated?

Answer 1

N=(4*5-1)*5*5*5=2375

where
4 cases of first digit {2,4,6,8} 
5 cases of second digit {0,2,4,6,8} 
1 case of 44 for two leftmost digit
5 cases of third digit {1,3,5,7,9}
5 cases of fourth digit {1,3,5,7,9}
5 cases of fifth digit {1,3,5,7,9}