F5 maths nCr nPr

1. Gary has 5 different cartons of drinks and 6 different cans of drinks. How many combinations are there if he is going to put 3 cartons of drinks and 4 cans of drinks into the refrigerator?
[Steps plz]

2. Among 10 students, half of them are male. A boy and a girl are now selected from them to form a group. How many different groups can be formed?
[Why the answer is 5P5 =120?]

3. 30 people are participating in a lucky draw of a carnival. Find the number of ways of awarding the first prize, the second prize, the third prize, the fourth prize and the consolation price to 5 of them.
[Why 30P5 not 30C5?]

4. There are 16 empty boxes in the figure.
__ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __
(a) To fill in any 4 boxes with blue colour, how many different patterns can be formed?
(b) Now we have 4 colour pens in red, blue, black and green.
(i) To fill in any 4 boxes with different colours, how many different patterns can be formed?
(ii) To fill in any 4 boxes by using each colour pen, how many different patterns can be formed?
[Steps plz, how to determine when to use nCr and when to use nPr?]