Multiple choice

The letters of the word "$INDEPENDENCE$" are arranged in all possible ways. Of these the number of words in which the '$D$'s come together is

  1. $11 !$
  2. $\displaystyle \frac {11 !}{4!}$
  3. $\displaystyle \frac{11!}{4! \: 3!} $
  4. $\displaystyle \frac{11!}{4! \: 3! \: 2!} $
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The word INDEPENDENCE has 12 letters: I(1), N(3), D(2), E(4), P(1), C(1). Treating the two D's as one unit, we have 11 items to arrange: I(1), N(3), E(4), P(1), C(1), (DD)(1). The number of arrangements is 11! / (3! * 4!).

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