A behavioral economist studies transportation habits in an urban center. She identifies 4 bus routes that connect to 3 different light rail routes available to participants in the study. Before she interviews participants, she must determine the number of possible routes participants can choose to use. Which expression represents the number of available options?
4!+3!
4×3
4!×3!
4!/3!
To determine the number of possible routes participants can choose to use, we need to calculate the number of combinations. Since there are 4 bus routes and 3 light rail routes available, we can use the multiplication principle to determine the total number of options.
The multiplication principle states that if there are n independent choices available for one event and m independent choices available for another event, then the total number of possibilities is the product of n and m.
Therefore, the expression that represents the number of available options is 4 × 3, which simplifies to 12.
clearly, 4!x3!
she can pick the 4 bus routes in any order. For each pick, she can assign the rail routes in any order.
Probably not practical in the real world, however...