How many three letter arrangements can be formed if a letter is used only once?

Question

Raven Higgins · Accepted Answer

Explanation:This is equivalent to asking in how many different ways can u select 3 from an available 5 and arrange them.This is then the permutation                                 5              P      3        =                  5        !                              (          5          -          3          )                !              =    60  .

Leonel Contreras · Accepted Answer

Step 1There are 5 ways to choose the first letter, 4 to choose the next letter and 3 ways to choose the third letter, hence       5    ×    4    ×    3    =    60   ways to choose an arrangement of 3 letters from 5.In general, if you have n distinct objects from which to choose an arrangement of k items then the number of ways you can do it is:                                n              P      k        =                  n        !                              (          n          -          k          )                !            Step 2In our example,       n    =    5  ,       k    =    3   and:                                5              P      3        =                  5        !                              (          5          -          3          )                !              =                  5        !                    2        !              =                  5        ×        4        ×        3        ×                                                                                                  2                                                                                      ×                                                                                                  1                                                                                                                                                                                            2                                                                                      ×                                                                                                  1                                                                                            =    5    ×    4    ×    3    =    60  If the order of the chosen items does not matter, then the number of ways to choose k items from n is:                                n              C      k        =          (                                    n                                                k                              )        =                  n        !                    k        !                  (          n          -          k          )                !

How many three letter arrangements can be formed if a

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