# 20 identical marbles of green colour and 20 identical marbles of white colour can be arranged in a row in how many ways so that no two same colour marbles are adjacent?

$\begin{array}{1 1} (20 \!)^ 2 \\ 2.(20 \!)^2 \\ 2\\ 1\end{array}$

Fix all the white marbles in one way (since the marbles are identical.)
Then fix all the green marbles in one way in between the white ones.
or
Fix all the green ones first and then fix the white ones in between the green ones.
in 1 way
$\therefore$ The required no. of arrangements = 1+1=2 ways.
answered Sep 5, 2013