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

Question

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 (A) 21600 (B) 43200 (C) 86400 (D) 151200

Tardigrade Admin · Accepted Answer

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 (6 ! × 5 !/2)=(720 × 120/2)=43200

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

21600

43200

86400

151200

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
$\frac{6 ! \times 5 !}{2} = \frac{720 \times 120}{2} = 43200$

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