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Roy must elect 3 courses from among 5 courses in group I and 4 courses in...

Roy must elect 3 courses from among 5 courses in group I and 4 courses in group II. If he must take at least 1 of his 3 electives from each group, how many choices does he have? (Hint: First find how many choices he has if he elects only 1 course from group I. Then find how many choices he has if he elects 2 courses from group I. Since he must do one or the other of these, the final answer is the sum of the two answers.)

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Answer #1

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total number of choices =9C3 =84

number of ways so that no course from group 1 or group 2 =5C3+4C3 =10+4 =14

hence number of choices such that at least 1 of his 3 electives from each group =84-14 =70

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