F.5 permutation

1. number of odd numbers between 300 and 800
=number of odd numbers with one of 3, 5, 7 as 100's digit
+number of odd numbers with one of 4, 6 as 100's digit
=3(100's digit)x4(units digit)x8(10's digit)+2(100's digit)x5(units digit)x8(10's digit)
=176

2. number of even numbers between 2000 and 7000
=number of even numbers with one of 3 as 1000's digit
+number of even numbers with one of 2, 6 as 1000's digit
=1x3x6+2x4x6
=66

3. number of 4-digit even numbers
=number of 4-digit even numbers with one of 1, 3, 7, 9 as 1000's digit
+number of even numbers with one of 2, 6, 8 as 1000's digit
=4x4x6+3x3x6
=150

2013-04-23 10:40:57 補充：
correction to Q.3

number of 4-digit even numbers
=7x8x8x4
=1792

2)
Case 1:
Thousands: 2 or 6 (2)
Units: 0, 2, 6, 8 excluding thousands digit (3)
Hundreds: rest 6 digits (6).
tens: rest 5 digits (5)

Case 2:
Thousands: 3 (1)
Units: 0, 2, 6, 8 (3)
Hundreds: rest 6 digits (6)
tens: rest 5 digits (5)

The required number
= 2x3x6x5 + 1x4x6x5
= 300 ... ans