How many different ways can the letters in the word ALGEBRA be arranged?

Answer 1

The word "ALGEBRA" consists of 7 letters, where the letter "A" appears twice. To find the number of different arrangements, we use the formula for permutations of multiset: ( \frac{n!}{n_1! \cdot n_2! \cdots n_k!} ). Here, ( n = 7 ) (total letters) and ( n_1 = 2 ) (for the letter A), resulting in:

[ \frac{7!}{2!} = \frac{5040}{2} = 2520. ]

Thus, there are 2,520 different ways to arrange the letters in the word "ALGEBRA."