Hello How do I see which photos are not in a collection? or know if the photo is in a collection ?

'Occam's Razor'. strikes again!

Similar to the reply from Conrad is this-

Simply have Badges turned 'on' for thumbnails. A 'Double page' badge icon indicates an image- IS in a Collection. (No Collection Badge- Not in a Collection.)

A [Left-Click] on the badge will show a list of the Collections where the image can be listed.

A [Left-Click] on a Collection Name in this list will take you to that specific Collection.

To see which collections a photo is added to, right-click the photo and look on the Go To Collection submenu. If you choose one of the listed collections, it will switch to that collection as the source for the current filmstrip/grid.

The answer from @dj_paige  is the correct answer.

His suggestion to use the characters "a e i o u" can be expanded as in my screen-clip.

Note there are spaces between the characters "a b c d e......" etc.

(but if you have a collection named @#$ this also fails to work)

To find photos not in a collection: Use a smart collection, set the criterion to

Collection does not contain a e i o u y (but if you have a collection named Z57, this fails to work)

If you really want to be comprehensive, use all letters and numerals

Turn on badges to see if a photo is in a collection. View->View Options