# How do you find the number of distinguishable permutations using the letters in FOOTBALL?

$10080$
There are $8$ letters, so there are 8! permutations. However, the question asks for distinguishable permutations, so you must eliminate the permutations presented by the repeated letters. There are $2$ O's and $2$ L's.
(8!)/(2! * 2!) = (8*7*6*5*4*3*2*1)/(2*1*2*1)=40320/4=10080