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TS EAMCET · Maths · Permutation Combination

All possible words (with or without meaning) that contain the word 'GENTLE' are formed using all the letters of the word 'INTELLIGENCE'. Then the number of words in which the word 'GENTLE' appears among the first nine positions only is

  1. A \(1440\)
  2. B \(5040\)
  3. C \(2520\)
  4. D \(720\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(1440\)

Step-by-step Solution

Detailed explanation

\( \text{Letters in INTELLIGENCE: I(2), N(2), T(1), E(3), L(2), G(1), C(1)} \) \( \text{Letters in GENTLE: G(1), E(2), N(1), T(1), L(1)} \) \( \text{Remaining letters: I(2), N(1), E(1), L(1), C(1)} \text{ (6 letters: I, I, N, E, L, C)} \)…