kramberol

2022-07-15

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

Camron Herrera

Expert

Explanation:
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 2O's and 2L's.
$\frac{8!}{2!\cdot 2!}=\frac{8\cdot 7\cdot 6\cdot 5\cdot 4\cdot 3\cdot 2\cdot 1}{2\cdot 1\cdot 2\cdot 1}=\frac{40320}{4}=10080$

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