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jmc

counting and probability senior

Problem

My grandpa has 10 pieces of art, including 3 prints by Escher. If he hangs the pieces of art in a row in a random order, what is the probability that all three pieces by Escher will be placed consecutively?
Solution
To count the number of ways of arranging the 10 pieces of art with the three Escher's consecutively, treat the three of them as one item. It is clear that we are then selecting the location of 1 item out of 8 total which can be done in ways. There are also a total of ways to place the three pictures without restrictions. Thus the probability that we want is .
Final answer
\dfrac{1}{15}