Are they in sequence? If so, check the little box to the left of the first one, then holding down the Shift key scroll down to the last one you want to get rid of. That will select everything in between as a block. Then just hit the trash can icon in the toolbar.
Sorry, does not work.
What happened when you tried @Latoque's suggestion?
When I selected the first email, and held down the mouse button while scrolling, it started moving the first email to another location. The key here is to not hold down the mouse button while scrolling.
It now works. Thank you for your indulgence.
What I'd like now is a way to delete permanently directly without having to go through TRASH.
No. There is no such option in the webmail UI.
Latoque is right. All you can do is select all at the top, then uncheck the ones you want to keep and delete the rest, then empty the trash. It's a confirmation saftey UI to give you one more chance to not delete something you really didn't intend to delete...
I will correct myself a bit---------there is an option to bypass the Trash folder in the settings. On the Inbox page click on the gear icon in the upper right corner then on Settings. Under Mail>>>>>>Common on the landing page you will see an option to "Permanently remove deleted emails". However-----all that does is bypass the Trash folder and send it straight to the "Dumpster". If you right-click on the Trash folder you will see the option to "Recover deleted items". Anything you delete winds up in that folder and will stay there for 30 days no matter how you got it there. You cannot delete from that folder. You have to wait for it to drop off after the 30 day period.