Use the digits 0-9, find out how many 4 digit numbers can be configured based on the stated conditions:

a. The number cannot start with zero and no digits can be repeated.

b. The number must begin and end with an odd digit. (Repeated digits are okay)

c. The number must at least 5000 and be divisible by 10. (Repeated digits are okay)

d. The number must be less than 3000 and must be even. No digits may be repeated in the last 3 digits. (That is, 2,234 would be okay but 2,334 would not be okay)

A) On the first place we can put 9 digits, on the second 9, on the third place 8 and on the last place 7 (because no digits can be repeated):

9 · 9 · 8 · 7 = 4536 numbers

b) There are 5 odd digits can be repeated. So:

5 · 10 · 10 · 5 = 2500 numbers

c) On the first place we can put:5,6,7,8,9 (5 digits) On the last place is just one (0), because the number must be divisible by 10:

5 · 10 · 10 · 1 = 500 numbers

d) on the first place we can put 2 digits (1, or 2 - there are no 4-digit numbers starting with 0). The last digit must be even, but the order can be:

X - odd - odd - even 2 · 5 · 4 · 5 = 200

X - odd - even - even 2 · 5 · 5 · 4 = 200

X - even - odd - even 2 · 5 · 5 · 4 = 200

X - even - even - even 2 · 5 · 4 · 3 = 120

Finally: 200 + 200 + 200 + 120 = 720 numbers