Question 15

Mathematics Permutation and Combination Medium

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

(A) 120
(B) 1228
(C) 720
(D) 24
✓ Correct Answer: Option D Verified Solution

📘 Step-by-Step Solution & Detailed Explanation:

The word is ``BANGLORE'' whose letters are \(B,A,N,G,L,O,R,E\) (all distinct). We require that the string ``ANGLE'' (the letters \(A,N,G,L,E\) in that order) appears together as a block. Treat ``ANGLE'' as one single item. Then the items to arrange are: \[ \{\text{ANGLE (block)},\,B,\,O,\,R\}, \] i.e. \(4\) distinct items. These can be arranged in \(4!\) ways. The block ``ANGLE'' has a fixed internal order, so there are no additional arrangements inside it. Hence the number of permutations is \[ 4! = 24. \] \[ \boxed{24} \]

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