The Growlies for Groups site recommends for a tossed salad for 50 you use 3 cucumbers so I guess 6 should cover it. They don't mention celery but I'd guess three or four good sized heads would be enough. You could get more and just keep them in the fridge to put out if the rest runs out.
Hope this helps.

How much you need is partly determined by what other food you have. If the veggie platters are the main thing, you will need more than if they are one of many food choices. What I usually do with veggie plates is to get more or less even amounts of stuff. It seems easier to arrange nicely that way. If I read your post correctly, and I may not have, I would get the same volume of cucumber and celery as you did of carrot and broccoli. If you haven't purchaced anything yet, I would assume each guest would have about 6 pieces total more or less divided equally. 150 pieces of each veggie. More if you want to ensure leftovers. Oh, and cherry tomatoes or olives are good accent bits to veggie platters.

I would get 2 celery and 6 medium cucumbers. Celery goes a long way, when you cut it into 1" pieces! I always cut celery into 1 or 2" pieces, then slice thru center, lengthwise. Assuming you're having more food than the veggie platter. Lots of older folks can't digest fresh veggies, y'know.

Hope your mother has a fun birthday!