In a matching problem, there are two columns. The first column has 4 statements whereas the second column has 5 statements. Every statement of the first column is to be matched with exactly one statement of the second column. In how many different ways can one student match the two columns if the student has no idea of the correct match?
120
Each of the 4 statements in Column I must be matched to a distinct statement in Column II (one statement of Column II is left unused), so the number of ways is the number of injective (one-to-one) mappings from a 4-element set into a 5-element set.
This equals \(^5P_4=5\times4\times3\times2=120\).
Hence, there are 120 different ways to match the two columns.
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