Tatiana has a special puzzle in which all of the pieces fit together in any way. There is no goal picture. Instead, the goal of the puzzle is to make different patterns and pictures using the pieces. If Tatiana has 50 unique puzzle pieces and she plans to use all of them, how many possible pictures can she create

An arrangement of things in a certain sequence is what we refer to as a permutation. The constituents or components of sets are presented in this section in a sequential or chronological fashion. A coming together or merging of several parts or characteristics in which each of the constituent parts or traits retains its unique identity.

Given that:

50 unique pieces of puzzle

Use them all to solve puzzle

No repetition is allowed therefore

Since no repetition is allowed because all puzzle pieces are required to be used.

Therefore each of the 50 pieces can be used max one time

Therefore if we start with piece like this " 1 2 3 .. up to ... 50 " it is one combination

Another could be "2 1 3 .. up to .. 50" or "3 1 2 .. up to 50" and so on

So we see that we can see that we can select the first piece in 50 ways 49 left which could be selected for second piece then 48, 47 respectively

Therefore 50X49X48X47X46X....X1 = 50!

Hence, It is an example of Permutation without repetition.

Learn more about permutation and combination here:

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Option is missing

A. Combination with repetition

B. Permutation with repetition

C. Combination without repetition

D. Permutation without repetition