Multiple choice

The number of ways in which all the letters of the word HUSSEY be arranged so that two S are never together is

  1. 240

  2. 120

  3. 360

  4. 480
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A Correct answer
Explanation

Total arrangements of HUSSEY (6 letters, 2 S's) = 6! / 2! = 360. Arrangements where S's are together: Treat (SS) as one unit. Arrangements of (SS), H, U, E, Y = 5! = 120. Total - Together = 360 - 120 = 240.

AI explanation

The word HUSSEY has 6 letters, which can be arranged in 6! = 720 ways without restriction. To ensure the two S letters are never together, we use the gap method, placing the 4 distinct non-S letters (H, U, E, Y) first in 4! ways. This creates 5 gaps, and we choose 2 of these gaps to place the S letters, giving 4! x (5 choose 2) = 24 x 10 = 240 arrangements.

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