Combinatorial selection with category constraints

Questions asking for the number of ways to select a specified number of items from multiple distinct categories where each category has a minimum or maximum constraint (e.g., select 2 pop CDs, 2 jazz CDs, and 1 classical CD).

2 questions

CAIE S1 2008 June Q3
3 Issam has 11 different CDs, of which 6 are pop music, 3 are jazz and 2 are classical.
  1. How many different arrangements of all 11 CDs on a shelf are there if the jazz CDs are all next to each other?
  2. Issam makes a selection of 2 pop music CDs, 2 jazz CDs and 1 classical CD. How many different possible selections can be made?
OCR MEI S1 2010 January Q6
6 Three prizes, one for English, one for French and one for Spanish, are to be awarded in a class of 20 students. Find the number of different ways in which the three prizes can be awarded if
  1. no student may win more than 1 prize,
  2. no student may win all 3 prizes. Section B (36 marks)