CAYLEY 2017 Problem 24

Three coins are placed in the first three of six squares, as shown.

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A move consists of moving one coin one space to the right, assuming that this space is empty. (No coin can jump over another coin, so the order of the coins will never change.) How many different sequences of moves can be used to move the three coins from the first three squares to the last three squares?

Answer Choices
A. 44
B. 40
C. 42
D. 48
E. 50