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

1 Answer
Fleur
Jul 10, 2017

#10080#

Explanation:

FOOTBALL

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#

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