Question

The number of arrangements of the letters of the word BANANA so that the arrangement starts and ends with the same letter, is

• A. 12
• B. 16
• C. 18
• D. 20
• E. 24

Hint:

Always list the letter counts first (B:1, A:3, N:2). This makes identifying possible start/end letters and the remaining permutations easier.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
The word BANANA has 6 letters: 3 A's, 2 N's, and 1 B.
We must find permutations that begin and end with the same letter.
Step 2: Key Formula or Approach:
The matching ends can only be A's or N's.
Case 1: Ends are A and A. Arrange the remaining letters (A, N, N, B).
Case 2: Ends are N and N. Arrange the remaining letters (A, A, A, B).
Sum the arrangements.
Step 3: Detailed Explanation:
Case 1: Word format is `A \_ \_ \_ \_ A`.
The inner letters to arrange are B, N, N, A.
Number of arrangements = \(\frac{4!}{2!} = \frac{24}{2} = 12\).
Case 2: Word format is `N \_ \_ \_ \_ N`.
The inner letters to arrange are B, A, A, A.
Number of arrangements = \(\frac{4!}{3!} = \frac{24}{6} = 4\).
Total arrangements = \(12 + 4 = 16\).
Step 4: Final Answer:
Option D.