Multiple choice

How many different words can be formed using all the letters of the word "PRECIOUSLY" if the letters P, R and E must always remain together?

  1. 2,41,920

  2. 4,02,140

  3. 32,400

  4. 45,320

  5. None of these
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A Correct answer
Explanation

Word "PRECIOUSLY" has 10 letters: P, R, E, C, I, O, U, S, L, Y. Treating PRE as one unit, we have 8 units (PRE, C, I, O, U, S, L, Y). These can be arranged in 8! ways. Within the unit PRE, the letters can be arranged in 3! ways. Total = 8! * 3! = 40320 * 6 = 241920.

AI explanation

The word PRECIOUSLY has 10 distinct letters, and treating P, R and E as a single unit gives 8 entities in total. These 8 entities can be arranged in 8! ways, and the letters within the unit can be arranged in 3! ways. Multiplying these gives 8! x 3! = 40320 x 6 = 241920.

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