The number of unique permutations of the word ALGEBRA is 5040. Hence, option A is the right choice.
Permutations are the process of selecting a set of a certain number of outcomes from the total outcomes. In permutation, the order of selection matters.
In the process of selecting r items from n items, where the order of selection matters, is given by permutation:
nPr = (n!)/(n-r)!.
In the question, we are asked to find the number of permutations of the word ALGEBRA.
The word ALGEBRA consists of 7 letters, and we are asked to find all unique permutations of this word.
Hence, we are asked to find the permutation of 7 letters from 7 letters and the order of selection matters, so it can be calculated by the formula:
nPr = (n!)/(n-r)!, where n = 7, and r =7.
7P7 = 7!/(7-0)! = 7!/0! = 5040/1 = 5040.
∴ The number of unique permutations of the word ALGEBRA is 5040. Hence, option A is the right choice.
Learn more about Permutations at
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