A bag contains 5 blue blocks, 7 green blocks, and 6 red blocks. Blocks are selected randomly, one at a time, from the bag. What is the minimum number of blocks that need to be removed from the bag to be certain that there are three that are the same colour?
Solution
The worst case scenario is that we draw 2 blue blocks, 2 green blocks, and 2 red blocks. After these six blocks are selected, regardless of the colour of the next block we will have three that are the same colour. This means that 7 blocks need to be removed to be certain that there are three of the same colour. How many blocks would need to be remove to ensure that three are the same colour if there were 10 blue blocks, 13 green blocks, and 4 yellow blocks to begin with?
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