Determine the number of distinguishable different words that can be formed by rearranging the letters for the following word? ALGEBRA

Question

a. 

630

b. 

2520

c. 

5040

d. 

1260

Answer 1

There are 7 letters in the word ALGEBRA, therefore they can be permuted in 7! ways.

However, for each permutation of all the letters, the two As can be

permuted between themselves without creating a new distinquishable word.

And those two As can be permuted in 2! ways.

Therefore the number of distinguishable words is

7!/2! = 2520