Single correct option
In how many ways can the letters of the word BANANA be arranged so that the two N's are NOT together?
- A. 36
- B. 40
- C. 44
- D. 60
Show answer and solution
Answer: (B) 40
Total arrangements = 6!/(3! × 2!) = 720/12 = 60 (there are three A's and two N's).
Arrangements with the N's together: glue NN into one block, leaving 5 items (B, A, A, A, NN), so 5!/3! = 20.
N's not together = 60 − 20 = 40.
Alternative (gap method): arrange B, A, A, A in 4!/3! = 4 ways. That creates 5 gaps, and choosing 2 of them for the N's gives C(5, 2) = 10. Total = 4 × 10 = 40. ✓
Arrangements with the N's together: glue NN into one block, leaving 5 items (B, A, A, A, NN), so 5!/3! = 20.
N's not together = 60 − 20 = 40.
Alternative (gap method): arrange B, A, A, A in 4!/3! = 4 ways. That creates 5 gaps, and choosing 2 of them for the N's gives C(5, 2) = 10. Total = 4 × 10 = 40. ✓
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