Question

The number of arrangements of the letters of the word $BANANA$ in which two $N^{\prime }s$ do not appear adjacently is

• A. $40$
• B. $60$
• C. $80$
• D. $100$

Answer 1

The correct option is A $40$

We can arrange $B,A,A,A$ in $\frac{4!}{3!}=4$ ways
For each arrangement of these four letters, there are five places (marked with $X$) for $N$ as shown below
$X-X-X-X-X$
We can choose two out of these five in ${}^5{C}_2=10$ ways.
Thus the required number of ways $=4\left(10\right)=40$