Exploring Minimum Count for At Least Two Different Objects in a Set

Author:
Lew W. S.
Start with 1-P 1-G 1-R (1-P means one purple grape, 1-G means 1 green grape and 1-R one red grape.

How many grapes must we take out (without looking), to have at least two grapes of different colours?

Then take 2-P, 2-G,2-R. Again ask "How many grapes do we take out (without looking) to have at least two grapes of different colours?"

Then we ask "What if we have 2-P, 2-G, and 3-R? How many grapes do we take out to be sure to have at least two grapes of different colours?"

Can you conclude how many grapes must you take out (without looking) to be sure you have at least two grapes of different colours for the question (a)?

For question (b) to be sure to take out all the grapes of the same colour (without looking) what do you think is the worst case? And so how many grapes must be taken out before we are sure to have all the grapes of a certain colour to be taken out?