We have, 10 Red and 5 Yellow roses of different sizes. Now, x= number of garlands that can be formed with all these flowers so that no two yellow roses come together =‌
1
2
(10−1)!×‌10P5 =‌
1
2
×9!×‌
10!
5!
=x=‌
10!
2
[‌
9!
5!
] ⇒‌‌‌
2x
10!
=‌
9!
5!
and y= number of garlands formed with all these flowers so that all the red roses coming together =‌