In how many different ways, the letters of the word ALGEBRA can be arranged in row if. The two As are together?

Options

A. 720
B. 620
C. 780
D. 1600

Answer

To solve the problem of arranging the letters of the word "ALGEBRA" with the condition that the two 'A's are together, we can follow these steps:

### Step-by-Step Solution:

1. **Treat the two 'A's as a single unit**: Since the two 'A's must be together, we can consider them as one single entity or unit. Let's denote this unit as "AA".

2. **List the remaining letters**: The letters in the word "ALGEBRA" are A, L, G, E, B, R, A. When we treat the two 'A's as one unit, we have the following units to arrange: AA, L, G, E, B, R. This gives us a total of 6 units to arrange.

3. **Count the total units**: The units we have are: AA, L, G, E, B, R. Therefore, we have 6 units in total.

4. **Calculate the arrangements**: Since all the units are distinct (the unit "AA" is treated as one letter), we can arrange these 6 units in \(6!\) (6 factorial) ways.

\[ 6! = 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 720 \]

5. **Final answer**: Therefore, the total number of different ways to arrange the letters of the word "ALGEBRA" with the condition that the two 'A's are together is **720**.