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How may permutations of the word “spell” are there? There are____________
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The number of permutations with repeats is \(\Large \frac{N!}{n_1!n_2!...n_k!}\) where N=total number of items k=number of types of items n1,n2...nk=number of items of each type. For unique items, put n=1 Note that \(\sum_1^k n_k = N\) Example: How many permutations can we form with the word parallel? there are 2a's, 1e, 3l's, 1p, 1r for a total of 8 letters. The permutation is therefore \(\Large \frac{8!}{2!1!3!1!1!}=\frac{40320}{2\times1\times6\times1\times1 }=3360\) See also following link if you need more explanations: http://www.mathwarehouse.com/probability/permutations-repeated-items.php
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