Question

There are 2 sisters among a group of 10 persons. In how many ways can the group be arranged around a circle so that there is exactly one person between the two sisters?​

Answer 1

Answer

fix one person and the brothers B1 P B2 = 2 ways to do so.

other 17 people= 17!

Each person out of 18 can be fixed between the two=18, thus, 2 x 17! x 18=2 x 18!

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I gave hear the example of Brothers,you can follow the method...

Answer 2

The  total number of ways  is $2\times8!$.

Step-by-step explanation:

Given:

There are 2 sisters among a group of 10 persons.

To Find:

The  total number of ways  can the group be arranged around a circle so that there is exactly one person between the two sisters,

Solution:

Number of ways a person who sits in between the two sisters can be selected = $8_{C} _{1$ .

The sisters can be arranged on either side of the person in $2!$ ways.

Number of ways arranging remaining 7 persons =$=7!$

Thus, the total number of ways  $=8_{C} _{1} \times 7!\times 2!$

                                                      $=8 \times 7!\times 2!$

                                                      $=8!\times 2!$

                                                      $=2\times8!$

Thus, the total number of ways $2\times8!$.

PROJECT CODE#SPJ2