Q1: In a bag are $5$ red stickers, $4$ blue stickers, and $3$ green stickers. Emily removes stickers from the bag one at a time, without looking into the bag. She stops when she has $3$ stickers of the same colour. What is the greatest number of stickers she could take out of the bag?
Q2: With the same details in the above question, How many stickers must she take in order to guarantee that she will have at least one of each colour?
It's been quite long time after I have done permutations and combinations. I tried with some intro learning of permutations, but could not come up with any idea of solving this problem. So explanations would be great.
For question 1 (12): it is clear that the maximum number of stickers that can be taken out of the bag is 12. This is because it may be the case where you choose all the red and blue stickers before picking the last 3 green ones, finally ending the draw. So you may very well pick EVERY sticker before picking 3 of each (4 + 3 + 5 = 12)
For question 2 (10): in order to guarantee 1 of each color, you would have to exhaust the options of 2 stickers, so that the next sticker has to be the last color, and you only need one of each, so you are done. In this case, you will need to pick 10 stickers to guarantee one of each color. This is because, if you have not already picked one of each color prior, then u must have picked 5 red stickers and 4 blue stickers, and the last one must be green.
These questions don't seem to require and combinations or permutations, rather are just problems pertaining to reason.