The number of ways of arranging 2 red,3 white | vedclass

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(C) First,arrange the $2$ red and $3$ white roses in a circle. The number of ways to arrange $5$ distinct items in a circle is $(5-1)! = 4! = 24$. The

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$1440$

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(C) First,arrange the $2$ red and $3$ white roses in a circle. The number of ways to arrange $5$ distinct items in a circle is $(5-1)! = 4! = 24$. There are $5$ gaps created between these $5$ roses. We need to place $5$ yellow roses in these $5$ gaps such that no two yellow roses are together. The number of ways to arrange $5$ distinct yellow roses in $5$ gaps is $5! = 120$. Since it is a garland,the clockwise and anti-clockwise arrangements are considered the same,so we divide by $2$. Total number of ways $= \frac{4! 	imes 5!}{2} = \frac{24 	imes 120}{2} = 1440$.

The number of ways of arranging $2$ red,$3$ white,and $5$ yellow roses of different sizes into a garland such that no two yellow roses come together is

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