Question

There are 20 persons among whom two are sisters. Find the number of ways in which we can arrange them around a circle so that there is exactly one person between two sisters? Please note that the exact position on the circle does not matter (no seat numbers are marked on the circle), and only the relative positions of the people matter

Answer 1

Answer:

Required number of ways is 18! .

Step-by-step explanation:

Given:

Total People = 20.

We need to find: Number of ways in which we can arrange them around a circle so that there is exactly one person between two sisters.

Number of ways in which 2 sisters can be placed =  2! = 2

Number of ways in which a person is selected in between them = 20 - 2 =  18

Now, Number of ways left 17 person is arranged in 17 places = 17!

Taking circular table implies clockwise and anti clockwise symmetry reduces the possible chances by half

.

So, Total number of ways = 2 × 18 × 17!× (1/2) = 18 × 17! = 18!

Therefore, Required number of ways is 18!