Number of arrangements of the letters of the word ‘BANANA’ in which two N’s do not appear adjacently is

BANANA

   The letters B, A, A, A can be Arranged in $\frac{4!}{3!}$ ways.

                              $-\mathrm{B}-\mathrm{A}-\mathrm{A}-\mathrm{A}-$

    There are 5 places to arrange 2 N's so that N's do not come together.

$\therefore$2 N's can be arranged in $\frac{5{\mathrm{P}}_2}{2!}$ ways.

No of ways $$\begin{gathered} =\frac{4!}{3!}\times \frac{5{\mathrm{P}}_2}{2!} \\ =4\times 10=40 \end{gathered}$$

                          option (1)