nCr and nPr 6(5m)

please help me 5 questions. I need steps. (solution at the bottom) thank you. 5 marks
1. 10 horizontal lines and 15 vertical lines are intersected. How many rectangles can be formed?
2. In a badminton tournament, any 2 players must play against each other twice. However, a player was quit after playing 4 matches due to injury. If a total of 60 matches were played finally, how many players were there originally?
3. Peter plans to deliver 12 packages to 12 different spots.
(a) 3 packages will be delivered to 3 spots in the same district, so they will be delivered successively. How many delivery sequences does he have now?
(b) Apart from the 3 packages mentioned in (a), there are 4 packages to be delivered to 4 spots in another district successively. How many delivery sequences does he have now?
4. Gordon has 10 game discs, where 6 of which are tactical games and 4 are action games. He has a disc rack which can hold 6 game discs. If Gordon selects 4 tactical game discs and 2 action game discs out of 10 game discs to be put on the rack, how many permutations are there?
5. Given 2 x 37 x 47 x 67 x 97 = 22 603 522. How many positive even factors of 22 603 522 are there? Hint: Is 2 x 37 a positive even factor? Is 2 x 47 x 67 a positive even factor?

Solutions:
1. 4 725
2. 9
3. (a) 21 772 800
3. (b) 725 760
4. 64 800
5. 16