There are 5 roads from Allen to baker, 7 roads from baker to Carlson, and 4 roads from Carlson to dodge. How many different routes from Allen to dodge by way of baker and Carlson are possible?

140 different routes

Step-by-step explanation:

The first path (Allan to Baker) has 5 different options, so there are 5 possibilities. After that, there are 7 possibilities from Baker to Carlson. Then, there are 4 possibilities from Carlson to Dodge. To find the total number of possibilities, we just need to multiply the number of possibilities of each track, so:

5 * 7 * 4 = 140 possibilities, that is, 140 different routes.

6

Step-by-step explanation:

This is a case of combination since the order does not matter, it only matters that there must be a marble in each one inside, therefore we must apply its formula.

xCn = n! / x! * (n - x)!

n, in this case it would be 4 because we must subtract 2 from the total 6, since there must already be one inside in each display case.

x = 2, since it is the number of showcases.

Replacing:

 2C4 = 4! / 2! * (4 - 2)! = 6

Which means that you can in six different ways.