Answer:
The worksheet limit of 17,179,869,184 (17.2 billion) cells was established in Excel version 2007 and was extended as the same limits found in version 2010.
The worksheet maximum size limits of version 2007 (and version 2010) provided columns A to XFD, which is 16,384 (2^14) columns; and 1,048,576 rows (2^20); therefore 16,384 x 1,048,576 = 17,179,869,184 (or 2^34).
Originally within each worksheet for all version prior to 2007 (e.g. 2003 and before) Excel provided columns A to IV, which is 256 (2^8) columns; and 65,536 rows (2^16); therefore 256 x 65,536 = 16,777,216 (2^24), or 16.8 million cells.