How many photos fit on a 4GB memory card in a 10-megapixel digital camera?

A 10-megapixel image in JPEG format takes up about 2,5 Mb of space (can vary depending on the quality of the photo). That means you should be able to fit about 1600 pictures on a 4Gb card.
Every digital camera displays the number of pictures you can store on the current card.
See also
How many pictures will a 1GB memory card hold at 5.1 mega pixels

A simple way to find out how many images you can have on any memory card is to turn on the camera and set the resolution and file sizes and see what it tells you. A number of things will dictate what size image you get. The first is the quality setting. On my camera I have a standard setting, a fine setting, extra fine setting, Raw plus JPEG, Raw and JPEG. With RAW images on a 2 gig card I get 398 images. With RAW/JPEG and on a large size (3008 x 2000 pixles) I get 298 images. This is because I get two sets of images. Setting it to RAW/JPEG and small file (1504 x 1000 pixles) I get 364 images. Setting my quality to EXTRA FINE and Large image (3008 x 2000 pixles) I get 613 images. My advice is to always shoot at either RAW or JPEG at the highest resolution. Storage capacity is so cheap nowadays it is hardly worth worrying about how many images you can get on a card