Drop down menu to populate multiple sheets

This is my first post and I've been searching trying to figure this out but havent had much luck...
I'm making a spreadsheet to organise classes & riders for a motorcycle race where I input the rider's number and name (in 2 separate colums) and then select from a drop down which class they are racing. They can ride up to 3 classes so there are 3 columns with the same drop down menu.
There are 10 classes to choose from in the drop down and each class has its own sheet. I have the drop down created already.
I want the rider number and corresponding name to show up on each class sheet where it has been selected from the drop down
...I hope that makes sense

I attached the file for reference

-it could be simplified if needed where just the name copies to the class sheet
Thanks in advance