How many ways can 6 people be seated in a round table if two people insist on sitting beside each other?

Example 1 In how many ways can 6 people be seated at a round table? Solution As discussed in the lesson, the number of ways will be (6 – 1)!, or 120. (i) A and B always sit together. (ii) C and D never sit together.

How many ways can six students line up if two students want to stand next to each other?

Candidates are lined up on stage behind podiums facing the audience. If two of the candidates refuse to be positioned next to each other, the candidates can be arranged in 480 different ways.

How many ways can 8 people be seated around a round table?

Hence total no of ways 8 persons can be seated around a round table such that 2 given persons are seated next to each other = 2*6! = 1440. A then B. Then 6! ways of seating the other 6 to right of B. Also consider B then A. Again 6! ways to the right of A. Total 6!+6!=2x 6!=2×720=1440.

How many ways can you make 6 people sit on 6 chairs?

Now our aim is to arrange the remaining 5 persons on the seats from B to F. If the question was to find the number of ways of making six people sit on six chairs, the answer would have been 6! which is equal to 6x5x4x3x2x1=720.

How many people do you need to seat at a party?

If there are 8 people and 2 need to sit next to each other you have 7 groups to seat. The 6 who are don’t care and the couple who need to sit together. So, starting from Left to right (or any order you want) you have 7 to choose from, and then the remaining 6 for the next spot, 5 for the next, till you have the last spot.

How many people are to be seated in a row?

9 people are to be seated in a row. Two of them, A and B, must sit next to each other, and another two, C and D, are not to be seated next to each other. How many different sitting arrangements are possible?