My teacher had 3 big boxes of sweets. Each box contained sweets of a different colour.

Q: My teacher had 3 big boxes of sweets. Each box contained sweets of a different colour. Each pupil was given 5 sweets of two different colours. If each pupil in the class received a different combination of colours, what was the largest possible number of pupils in the class?
A. 8
B. 12
C. 16
D. 64

Answer: B

Assume the three colours are red, blue and yellow. There are only 4 different combinations for any two colours. So, for red and blue the combinations are:

  • R R R R B
  • R R R B B
  • R R B B B
  • R B B B B

There are 3 ways to choose 2 out of 3 colours:

  • red-and-blue,
  • blue-and-yellow
  • red-and-yellow

So the different colour combinations for 5 sweets is 4 × 3 = 12 combinations. Hence, the largest possible number of pupils is 12.