Question: M&Ms are "colorful button shaped chocolates." Suppose that from our point of view as a consumer, each M&Ms: M&Ms is equally likely to have one of c different colors. We randomly sample 3 M&Ms: the two have the same color, whereas the third M&M has a color different from the first tow.
Find the maximum likelihood estimate for c.
We sample a fourth M&M which happens to have a color different from the colors we have seen so far in our sample. Taking this new data into consideration, what is now the maximum likelihood estimate for c?