The number of different ways of preparing a garland using 6 distinct white roses and 5 distinct red roses such that no two red roses come together, is 
 

Number of white roses=6

Number of red roses=5

6 white roses can be arranged in a circular order in 5! ways

There are 6 places in between white roses . 5 red roses can be arranged in the 6 places in ${ }^6{P}_5$ ways.

$\text{Number of garlands}=\frac{5!\left({ }^6{P}_5\right)}{2}=\frac{120\times 720}{2}=43,200$