The number of arrangements, of the letters of the word MANAMA in which two M's do not appear adjacent, is
The number of arrangements, of the letters of the word MANAMA in which two M's do not appear adjacent, is
40
60
80
100
Solution
There are 6 letters.
M repeats 2 times,
A repeats 3 times.
We first arrange all letters except $2 \mathrm{M}^{\prime} \mathrm{s}$ in $\frac{4!}{3!}$ $=4$ ways
These 4 letters create 5 gaps, where we can arrange $2 \mathrm{M}^{\prime} \mathrm{s}$ in $\frac{{ }^5 \mathrm{p}_2}{2!}=10$ ways
$\therefore \quad$ Required number of arrangements $=4 \times 10=40$