Permutations and Combinations
Permutations with Restrictions
IIT-JEE 2002 Screening
Grade 11
Question:
The number of arrangements of the letters of the word BANANA in which the two N's do not appear adjacently is:
(1) $40$
(2) $60$
(3) $80$
(4) $100$
Step-by-Step Solution
Key Concept: Total arrangements $= \frac{6!}{3! 2!} = 60$ ($A$ repeats 3 times, $N$ twice). Arrangements with N's adjacent: treat $NN$ as one block $\Rightarrow \frac{5!}{3!} = 20$. Required $= 60 - 20 = 40$.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (1)