Single correct option
In how many distinct ways can the letters of the word SYSTEM be arranged so that the two S's are not next to each other?
- A. 360
- B. 300
- C. 240
- D. 180
Show answer and solution
Answer: (C) 240
Total arrangements of SYSTEM (S repeated twice, Y, T, E, M distinct) = 6!/2! = 360.
Arrangements with the two S's together: treat SS as one block → 5 units (block, Y, T, E, M), all distinct → 5! = 120.
Required = 360 − 120 = 240.
Check by gap method: arrange Y, T, E, M in 4! = 24 ways; this creates 5 gaps, choose 2 for the S's: C(5,2) = 10; total 24 × 10 = 240 ✓.
Arrangements with the two S's together: treat SS as one block → 5 units (block, Y, T, E, M), all distinct → 5! = 120.
Required = 360 − 120 = 240.
Check by gap method: arrange Y, T, E, M in 4! = 24 ways; this creates 5 gaps, choose 2 for the S's: C(5,2) = 10; total 24 × 10 = 240 ✓.
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