Six lectures, one each on algebra, astronomy, biology, economics, geology, and music, are to be scheduled in six consecutive periods. The biology lecture must be scheduled in the third period, and neither the algebra lecture nor the music lecture can be scheduled in a period immediately before or immediately after the biology lecture. How many different schedules are possible?
Select one answer.
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Answer: B ()
Since the biology lecture is scheduled in the third period, the algebra and music lectures cannot be scheduled in the second or fourth period. Thus, these two lectures must occupy two of periods 1, 5, and 6. There are 3 choices for the period containing the algebra lecture and 2 choices for the period containing the music lecture. The remaining 3 lectures can be assigned to the remaining periods in , or , ways. Therefore, the number of possible schedules is . The correct answer is Choice (B).