Table of Contents
- 1 How many ways can 7 persons be seated at a round table?
- 2 How many ways are there for 7 people to sit in a row if two people have to sit at least two seats apart?
- 3 How many ways can 5 children seated in a round table?
- 4 How many ways can 7 people be arranged into 7 chairs?
- 5 How many ways can 3 men be seated in 3 seats?
How many ways can 7 persons be seated at a round table?
Complete step-by-step answer: Since in this question we have to arrange persons in a circle and 7 persons have to be arranged in a circle so that every person shall not have the same neighbor. Hence there are 360 ways to do the above arrangement and therefore the correct option is A.
How many ways can 6 ladies be seated in a circular table such that two of the ladies must always sit 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.
How many ways 6 children could sit on a round swing when 2 of them always sit together?
Thus, the total of ways you can arrange their seats is 24 * 2 = 48 ways.
How many ways are there for 7 people to sit in a row if two people have to sit at least two seats apart?
That can be done in 2⋅6! =1440 ways.
How many ways can we place 7 apples in a circle?
The number of ways that 7 people can form a circle is 5,040.
How many ways can 6 boys and 6 girls be seated at a round table of 4 particular girls must sit together?
8*7*6*5=5040*1680=8,467,200 total possible arrangements. Originally Answered: How many ways can 6 boys and 6 girls be seated at a round table if 4 particular girls must not sit together?
How many ways can 5 children seated in a round table?
24
In how many different ways can five people be seated at a circular table? So the answer is 24.
How many ways that a family of 5 can be seated around a circular table with 5 chairs *?
Answer: If the symmetry of the table is not taken into account the number of possibilities is 5! = 120.
How many ways can 6 persons be seated at a round table?
So the number of ways 6 people can be seated around a round table becomes 1x5x4x3x2x1=120.
How many ways can 7 people be arranged into 7 chairs?
5040 ways
So there are 5040 ways of arranging seven people in a row of seven chairs.
How many ways can you seat A and B together?
(ii) C and D never sit together. Solution (i) If we wish to seat A and B together in all arrangements, we can consider these two as one unit, along with 3 others. So, effectively we’ve to arrange 4 people in a circle, the number of ways being (4 – 1)! or 6. Let’s take a look at these arrangements:
How many ways can C and D be seated together?
Similar to (i) above, the number of cases in which C and D are seated together, will be 12. Therefore the required number of ways will be 24 – 12 or 12. Example 3 In how many ways can 3 men and 3 women be seated at around table such that no two men sit together?
How many ways can 3 men be seated in 3 seats?
Now that we’ve done this, the 3 men can be seated in the remaining seats in 3! or 6 ways. Note that we haven’t used the formula for circular arrangements now. This is because after the women are seated, shifting the each of the men by 2 seats will give a different arrangement.
How many ways can you seat 3 women on a plane?
We’ll first seat the 3 women, on alternate seats, which can be done in (3 – 1)! or 2 ways, as shown below. (We’re ignoring the other 3 seats for now.) Note that the following 6 arrangements are equivalent: That is, if each woman shifts by a seat in any direction, the seating arrangement remains exactly the same.