A medium question on combinations for P2–P4, with a step-by-step solution, diagrams and the answer. Counting arrangements and choices appears in the Hua Xia Cup from the P1 and P2 first rounds to the P5 finals.
The question
There are 3 roads from Ming's home to the library and 2 roads from the library to school.
There is also 1 road from home to school that doesn't pass the library.
Ming never doubles back.
How many different ways can Ming walk from home to school?
Show the hints (2)
💡Hint 1: Split the ways into two kinds: through the library, and not.
💡Hint 2: Through the library: every road on the first leg can be followed by every road on the second.
Worked solution
Have a go first, then read the solution step by step.
1.Through the library: each of the 3 roads on the first leg can be followed by any of the 2 roads on the second, 3 × 2 = 6.
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