Hello, delicate_tears!

Let = number of 6-, 10-, and 15-passenger taxis, respectively,

. . where: .

We have: .

. . Hence: . .[1]

Since is an integer, .

. . Then [1] becomes: .

Since , then: .

It seems that there are: . possible choices.

However, if , then . . . not allowed.

Therefore, there are ways.