If 7 integers are selected from between 1 and 12 inclusive m

If 7 integers are selected from between 1 and 12 inclusive, must at least one of them be odd? Why? If 10 integers are selected from between 1 and 20 inclusive, must at least one of them be even? Why?

Solution

2. from 1 to 12 have 6 odd and 6 even numbers, hence when we are selected 7 integers from 1-12, must at least one of the odd.

from 1 to 20 have 10 odd and 10 even numbers, hence when we are selected 10 integers from 1-20, not must has any even number.