You can delete all the email messages from your inbox in just a few steps.
Delete all email from your inbox
Select the check box above the message list.
In the reading pane, select Empty folder. All your email will be moved to the Deleted Items folder.
Note: If you have Focused inbox selected, you will only empty your Focused inbox. Select your Other inbox to empty that too.
Empty your Outlook.com Deleted Items
To delete the messages, select the Deleted Items folder and select Empty folder.
To permanently purge all of your Deleted Items you need to also delete all of your recoverable items:
Open your Deleted Items folder.
Select Recover items deleted from this folder.
Select Empty folder.
Warning: Items removed from your recoverable items are permanently deleted and cannot be restored.