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jmc

counting and probability intermediate

Problem

How many ways are there to assign each of 6 friends to either the chemistry class or the biology class if one of these six, Manoj, refuses to be in a class without any of his friends?
Solution
For each friend, there are 2 choices for which class to place them in. Since this choice is independent for each of the 6 friends, we multiply the number of choices together. Hence there are ways to split the friends into two classes. However, 2 of those 64 arrangements are invalid: we can't put Manoj in chemistry and everyone else in biology, and we can't put Manoj in biology and everyone else in chemistry. So our final answer is .
Final answer
62