The number of different ways of preparing a g | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) First,arrange the $6$ distinct white roses in a circle. The number of ways to arrange $n$ distinct items in a circle is $(n-1)!$. So,$6$ white ros

Vedclass · Accepted Answer

$43200$

Vedclass · Answer

(A) First,arrange the $6$ distinct white roses in a circle. The number of ways to arrange $n$ distinct items in a circle is $(n-1)!$. So,$6$ white roses can be arranged in $(6-1)! = 5! = 120$ ways.There are $6$ gaps created between these $6$ white roses. We need to place $6$ distinct red roses in these $6$ gaps so that no two red roses are together. The number of ways to arrange $6$ distinct red roses in $6$ gaps is $6! = 720$ ways.Since it is a garland,the clockwise and anti-clockwise arrangements are considered the same. Therefore,we divide the total number of linear arrangements by $2$.The total number of ways $= \frac{5! 	imes 6!}{2} = \frac{120 	imes 720}{2} = \frac{86400}{2} = 43200$.

The number of different ways of preparing a garland by using $6$ distinct white roses and $6$ distinct red roses such that no two red roses come together is

Similar Questions

In how many ways can $7$ women and $7$ men be seated around a circular table such that each woman is seated next to a man?

$4$ gentlemen and $4$ ladies are to be seated at a round table. What is the probability that they sit alternately?

The number of ways in which $5$ boys and $4$ girls can sit around a circular table such that no two girls sit together is:

If $3$ sisters and $8$ brothers are together playing a game,then the number of ways in which all the sisters and brothers are to be seated around a circle such that all the $3$ sisters are not seated together is

If $n$ persons are seated around a circular table,what is the ratio of the unfavorable probability to the favorable probability that two specific persons sit together?

Vedclass Test Series

Exam Paper Generator

Online Exam Module