Question 1162510
There are 9 letters
But, there are 2 A's, 2 E's, 2 L's, and 2 P's:

so the number of unique (distinguishable) outcomes is:<br>

{{{ 9!/ (2!*2!*2!*2!) }}} = 22680<br>

Obtaining 'APPELLATE' is just one of those unique outcomes, so <br>
P('APPELLATE') = 1/22680  (about 0.0000441)