Find the number of different ways of preparing a garland using 7 distinct red roses and 4 distinct yellow roses such that no two yellow roses come together.

Explanation

First arrange 7 red roses in a circular from (garland form) in (7-1)! =6! Ways. Now, there are 7 gaps and 4 yellow roses can be arranged in these 7 gaps in `4""^(7)P_(4)` ways.
Thus, the total number of circular permutations is `6! Xx ""^(7)P_(4)`.
But, in the case of garlands, clock-wise and anti-clock-wise arrangements look alike. Hence, the number of required ways is.
`(1)/(2) (6! xx ""^(7)P_(4))`