If 5 red roses and 5 white roses of different | vedclass

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Question

(B) Total number of ways to arrange $5$ red and $5$ white roses in a garland is the number of ways to arrange $10$ distinct items in a circle,which is

Vedclass · Accepted Answer

$\frac{1}{126}$

Vedclass · Answer

(B) Total number of ways to arrange $5$ red and $5$ white roses in a garland is the number of ways to arrange $10$ distinct items in a circle,which is $(10-1)! = 9!$. Since the roses are of different sizes,we consider them distinct. For the roses to be placed alternately,we first fix the $5$ red roses in a circle in $(5-1)! = 4!$ ways. This creates $5$ gaps between the red roses. We can place the $5$ white roses in these $5$ gaps in $5!$ ways. Thus,the number of favorable arrangements is $4! 	imes 5!$. The probability is $\frac{4! 	imes 5!}{9!} = \frac{24 	imes 120}{362880} = \frac{2880}{362880} = \frac{1}{126}$.

If $5$ red roses and $5$ white roses of different sizes are used in preparing a garland,the probability that red and white roses come alternately is

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