What type of counting problem is this?
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?
A. Combination with repetition
B. Permutation with repetition
C. Combination without repetition
D. Permutation without repetition
Answers
Combination without repetition
hope it help ❣
Answer: It is an example of Permutation without repetition.
Permutation: 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. For instance, the number of possible permutations for the set A=1,6 is 2, such as "1,6," "6,1." As can be seen, there is no alternative possible configuration for the components that make up set A.
Combination: A coming together or merging of several parts or characteristics in which each of the constituent parts or traits retains its unique identity.
Step-by-step explanation:
Step 1: Given
50 unique pieces of puzzle
Use them all to solve puzzle
No repetition is allowed therefore
Step 2: Total Number of potential passcode
- 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.
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