I am sitting my A level exams (MEI) and I was looking through the S1 past papers and I encountered this question in the January 2010 paper:
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
(i) no student may win more than 1 prize,
(ii) no student may win all 3 prizes.
I tried to do part 1 using combinations, ie: 20 choose 3, but that didn't work. I couldn't even attempt part 2.
The right answers are:
(i) 20 × 19 × 18 = 6840
(i) (20^3) – 20 = 7980
Could someone please explain to me how these answers have been reached? The paper is at http://www.mei.org.uk/files/papers/s110ja_4766rev.pdf in case you want to see it. Mark scheme is at the end.