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  4. 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

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Q. 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

AP EAMCETAP EAMCET 2017

Solution:

We have 6 distinct white roses and 5 distinct red roses.
Total number of way making a garland such that no two red roses come together is
$\frac{6 ! \times 5 !}{2}=\frac{720 \times 120}{2}=43200$