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anonymous
 one year ago
Permutation: how many four letter word can you make out of SUMMER?
anonymous
 one year ago
Permutation: how many four letter word can you make out of SUMMER?

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Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.2numbers of permutations of n elements are: \[\Large n!\]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.2we have to count how many subset of four elements I can make with 6 elements

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0How would I do that?

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.2more precisely, we have to count how many subsets of four elements, we can make with 6 elements, being those subset different by the order of their elements or by the type of elements. In general, if we want to get howm many k elements subsets we can form with n elements, we have to apply this formula: \[\large {D_{n,k}} = n \cdot \left( {n  1} \right) \cdot \left( {n  2} \right) \cdot \left( {n  3} \right) \cdot ... \cdot \left( {n  k + 1} \right)\] Now, in your case k=4 and n=6

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.2\[\Large {D_{n,k}}\] isa called the numbers of simple dispositions

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so is it 5 P 4 + 6 * 4 P 2?

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.2if we apply my formula above, we get: \[\Large \begin{gathered} {D_{n,k}} = n \cdot \left( {n  1} \right) \cdot \left( {n  2} \right) \cdot \left( {n  3} \right) \cdot ... \cdot \left( {n  k + 1} \right) = \hfill \\ = 6 \cdot 5 \cdot 4 \cdot 3 = ...? \hfill \\ \end{gathered} \]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.2\[\large \begin{gathered} {D_{n,k}} = n \cdot \left( {n  1} \right) \cdot \left( {n  2} \right) \cdot \left( {n  3} \right) \cdot ... \cdot \left( {n  k + 1} \right) = \hfill \\ = 6 \cdot 5 \cdot 4 \cdot 3 = ...? \hfill \\ \end{gathered} \]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.2sorry for my first post, I have misunderstood your question!

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Ahah no worries :) tyyy
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