Question

In how many ways can 7 persons be seated at a round table if 2 particular persons must not sit next to each other?

Answer 1

Number of ways in which 7 people can be seated around a round table without any condition is 6!.

Now, let us assume these two particular people ALWAYS sit together and let us consider them as one unit.

Number of ways in which 6 people can be arranged around a round table is 5! And the two particular peopke can be arranged betwern them selves in 2! = 2 ways.

Hence, number of ways in which 7 people can sit around a round table where the two people must not sit together is :

6! - (5! X 2) = 120 x 4 = 480

Answer 2

Answer:

The answer is 480

Given problem:

In how many ways can 7 persons be seated at a round table if 2 particular persons must not sit next to each other?

Step-by-step explanation:

Given number of persons = 7

Note: Number ways 'n' persons can be seated at round table =(n-1)!  

therefore, number of ways 7 can be seated = (7-1)!

                                                                         = 6!  = 6×5×4×3×2×1 = 720  

here we need to find number ways 7 persons can be seated if 2 particular persons must not sit next to each other

First, find number of ways if two particular person (out of 7) sit together

Let assume that 1, 2, 3, 4, 5, 6 and 7 are the 7 persons

Take 1 and 2 as one unit

⇒ (1,2), 3, 4, 5, 6  [ here number of persons will be 5 ]

Number of ways 5 persons are sit together = 5!

And number of ways 1, 2 can be seated among them = 2!

Now, number of ways if two particular person sit together = 5!×2! =

                              = 5 × 4 × 3 × 2 × 1 × 2 × 1 = 240

Therefore, number ways 7 persons can be seated if 2 particular persons must not sit next to each other = 720 - 240 = 480