Utilizing every character in the string “NOKIA”, how many distinct strings can be constructed starting with N and terminating with A?
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Answer: B. 6
Explanation
Fixing the letter N at the beginning and the letter A at the end leaves three interior character positions. Arranging the remaining three interior letters (O, K, and I) without repetition uses factorial permutations. Calculating 3 factorial gives 3 times 2 times 1, which equals exactly 6 distinct possible strings. Permutations count the number of possible arrangements for a given set of distinct items. Factorial notation represents the product of all positive integers less than or equal to a given number. Fixed character constraints reduce the pool of movable elements available for permutation calculations.
Option A underestimates the total permutations by failing to account for all arrangements of the interior letters. Option C calculates permutations for all five characters without accounting for the fixed start and end constraints. Option D represents the full 5-factorial arrangement of all characters without any fixed position constraints.
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- Mathematics
- Category
- Mathematics
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- Difficulty
- medium
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