What is both possible and impossible at the same time?

You along with your friend are standing in front of two houses. Each of those houses inhabits a family with two children.

Your friend tells you the below two facts:
1) On your left is a family that has a boy who likes accounts but the other child loves science.
2) On the right is a family with a seven-year-old boy and a newborn baby.

You ask him, "Does either of the family have a girl?"

To this, he replies, "I am not quite sure. But can you guess that? If you are right, I will give you $500."

Which family do you think is likely to have a girl?

The more of this there is, the less you see. What is it?

Paul's height is six feet, he's an assistant at a butcher's shop and wears size 9 shoes. What does he weigh?

Which of the following words don't belong in the group and why?
CORSET, COSTER, SECTOR, ESCORT, COURTS

There are five vowels (a, e, i, o, u) in the English language.
Can you tell us a word that contains all these vowels?

I know a ten-letter word in the English language which can be typed using only the top rows of the computer keyboard.

The day after tomorrow will be three days before Tuesday. Can you find out what is today?

The doctor prescribed you to take one pill from the bottle every half an hour. The bottle is now left with only three pills.

How long do you think you have before you run out of pills?

0 0 0 = 6
1 1 1 = 6
2 2 2 = 6
3 3 3 = 6
4 4 4 = 6
5 5 5 = 6
6 6 6 = 6
7 7 7 = 6
8 8 8 = 6
9 9 9 = 6

You can use any mathematical symbols in the space provided to make all above algebraic expressions true.