Or something about holding down the <ALT> key while typing in the three digit ASCI code for the symbol you desire. Google ASCI Code and ALT and you'll find the list of them...
ALT + CTRL + T Once you go into the More symbols menu(via insert tab, symbols button), with most of the available symbols, MS word will display their shortcut keys.
On modern day Microsoft keyboards there are 119 keys. I counted them myself but that might not be the right number I might've counted wrong but I'm pretty sure that's right, 119 keys on a modern day...