Systematic listing and the product rule for counting

9 3-digit integers are made using three different digits. The digits are chosen from 1, 2, 3, 4, 5, 6, 7, 8, 9

How many more odd integers than even integers can be made?

A set of 4-digit integers each have a first digit greater than 6 and a second digit less than 8

What is the greatest possible number of integers in the set that are multiples of 5 ?

Five-digit integers are made using

1 2 7 8 9

For each integer, all the digits are used exactly once. The integers are greater than 40 000 and odd.

How many different integers can be made? You must show your working.

How many integers between 200 000 and 400 000 can be formed using only the digits

1 2 3 5 8 9

with no repetition of any digit?