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 a. 4!+3!
b. 4×3
c.4!×3!
d. 4!/3!

Total possible routes participants can choose = 4×3 = 12 ways

The correct option is - b. 4×3

Step-by-step explanation:

Given - 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.

To find - 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.

Proof -

Given that ,

Total bus routes = 4

So, number of possible ways she use the bus route = 4

Also,

The 4 bus route connects to 3 different light rail

So, possible ways that she use light rail = 3

∴ we get

Total possible routes participants can choose = 4×3 = 12 ways

The correct option is - b. 4×3

a - base

b - exponent

so,