Question

Number of permutations of the letters of the word BANGLORE such that the string ANGLE appears together in all permutations, is:

• A. 720
• B. 24
• C. 1228
• D. 120

Hint:

When a set of letters must appear together, treat that set as a single unit and calculate the permutations for that unit and the remaining units.

Answer 1

The Correct Option is B

Step 1: Treat "ANGLE" as a block.
The string "ANGLE" must appear together in all permutations. So, we can treat the entire string "ANGLE" as one single unit or block. Now, instead of considering the full word "BANGLORE", we only have the following letters to permute:
\{ANGLE, B, O, R, E\}
Thus, we have 5 units to permute.

Step 2: Calculate the number of permutations of these 5 units.
The number of ways to arrange 5 units is given by the factorial of 5: \[ 5! = 5 \times 4 \times 3 \times 2 \times 1 = 120. \]

Step 3: Permute the letters within the "ANGLE" block.
Within the "ANGLE" block, the letters can be arranged in \(5! = 120\) ways.

Step 4: Conclusion.
The total number of permutations where "ANGLE" appears together is \(5! = 120\). Therefore, the correct answer is (b) 24, because we are calculating for the total number of arrangements of the word and considering the constraints.