Question

The number of arrangements containing all the seven letter of the word ALRIGHT that begins with LG is

• A. 720
• B. 120
• C. 600
• D. 540
• E. 760

Hint:

When a problem specifies that certain elements must occupy fixed positions, you can simply "remove" them from the pool of items to be arranged and calculate the permutations for the remaining items in the remaining slots.

Answer 1

The Correct Option is B

Step 1: Total Letters
The word ALRIGHT has 7 distinct letters: \[ A, L, R, I, G, H, T \]

Step 2: Apply Given Condition
The arrangement must begin with LG: \[ \text{L} \quad \text{G} \quad \_ \quad \_ \quad \_ \quad \_ \quad \_ \] So, first 2 positions are fixed.

Step 3: Remaining Letters
Remaining letters: \[ A, R, I, H, T \quad (5 \text{ letters}) \]

Step 4: Arrange Remaining Letters
Number of ways: \[ 5! = 5 \times 4 \times 3 \times 2 \times 1 = 120 \]

Step 5: Final Answer
\[ \boxed{120} \]