Question

in how many ways can 20 person sit around a circle such that there is exactly one person between A and B​

Answer 1

in 2 * 18! ways 20 person can sit around a circle such that there is exactly one person between A and B​

Step-by-step explanation:

Two Persons  A  & B

Let say one person between A & B

is X

X can be selceted in 18 Ways  ( as there are 18 more people)

A  X B    and  B  X  A  are two arrangements

Hence Ways =  18 * 2

Now we we have 17 People left  & one group (AXB or BXA)

these can be arranged in 17!  Ways

so total number of ways = 18 * 2 * 17!

= 2 * 18!

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Answer 2

Answer:

The ways are= 18!×2!

Step-by-step explanation:

We know that n objects can be arranged around a circle in (n - 1)!

If it is regulated

'

n

'

 Things that are consecutive or counterclockwise mean the same thing, then the number of arrangements becomes half of that number.

i.e. number of arrangements = (n - 1)! × 2

Let there be exactly one person between two people (A and B), as stated in the question.

Then there are 17 more and this block of three people stands in a circle.

The number of ways to place 18 items in a circle is 17! manners.

Now A and B can be arranged on both sides of the person sitting between the 2! manners. The person sitting between A and B can be any of the 18 in the group and can be selected in 18 ways.

The total number of modes is therefore 18 × 17! × 2! = 18! × 2!

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