There are 10 red and 5 yellow roses of different sizes. If x is the number of garlands that can be formed with all these flowers so that no two yellow roses come together and y is the number of garlands formed with all these flowers so that all the red roses coming together, then 2 x - y 10 ! =

Step-by-step solution

Given that 10 Red roses & 5 Yellow roses. x is number of garlands that can be formed with all these flowers so that no two yellow roses come together. i.e., first arranging 10 Red roses in 9 ! 2 then in that 10 gaps we can arrange these 5 yellow roses in 10 ! 5 ! = 10 × 9 × 8 × 7 × 6 . So x = 9 ! 2 × 10 P 5 y is number of garlands with all these flowers so that all the red roses coming together. i.e., taking all red roses as one unit and arranging red and yellow roses is y = 5 ! 2 × 10