Your example is very correct. But the point you illustrated is not the point at issue.
The following example may illustrate the point:
Let's say there are 9 balls marked with 1, 2, 3,..., 9 respectively. There is a quessing game played between Jack and Jill. Jill can take any number of balls and make a number for Jack to guess what the number is. But Jack does not know how many balls Jill will take out of the 9 balls (Jill might take only 1, or any 2 in any order, any 3 in any order, etc.).
Is it easier for Jack to guess what the number Jill might have 1). if Jill can take any number of balls or 2). if Jill tells Jack that she will take only 5 or more balls to make the number?
