Multiple choice

The number of permutations of the letters of the word 'INDEPENDENCE' taken 4 at a time so that all the 4 are different is

  1. $24$
  2. $120$
  3. $240$
  4. $360$
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D Correct answer
Explanation

INDEPENDENCE has letters: I(1), N(3), D(2), E(3), P(1), C(1). Total distinct letters = 6 (I, N, D, E, P, C). We need to choose 4 different letters from these 6: 6C4 = 15. Arrange them: 15 * 4! = 15 * 24 = 360.

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