Garlands are formed using 6 red roses and 6 yellow roses of different sizes. The number of arrangements in garland which have red roses and yellow roses come alternately is

6 red roses can be arranged along a circle in 5! Ways. There are 6 places between the red roses 6 yellow roses can be arranged in the 6 places in 6! Ways.

     No of permutations $=\frac{1}{2}(5!\times 6!)$