Multiple choice

The number of seven letter words that can be formed by using the letters of the word $SUCCESS$ th at the two $C$ are together but no two $S$ are together is

  1. $24$
  2. $36$
  3. $54$

  4. none of these
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A Correct answer
Explanation

Word SUCCESS: S=3, U=1, C=2, E=1. Total 7 letters. Two C's together (treat as one unit CC). Remaining letters: S, S, S, U, E. We have 6 units: {CC}, S, S, S, U, E. To have no two S together, place S in gaps between other units. There are 4 non-S units (CC, U, E). Gaps: _ X _ X _ X _ (4 gaps). Choose 3 gaps for 3 S: 4C3 = 4. Arrange the 4 non-S units: 3! (CC, U, E) = 6. Total = 4 * 6 = 24.

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