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

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

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Answer 1 · 2017-07-10T21:52:23

$10080$ $10080$

Explanation:

FOOTBALL

There are $8$ $8$ letters, so there are $8!$ $8!$ permutations. However, the question asks for distinguishable permutations, so you must eliminate the permutations presented by the repeated letters. There are $2$ $2$ O's and $2$ $2$ L's.

$\frac{8!}{2! \cdot 2!} = \frac{8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}{2 \cdot 1 \cdot 2 \cdot 1} = \frac{40320}{4} = 10080$ $(8!)/(2! * 2!) = (8*7*6*5*4*3*2*1)/(2*1*2*1)=40320/4=10080$

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

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