How many ways can you arrange n objects in a straight line?

The number of ways N people can be arranged in a straight line without restriction = N! = (N – 1) * 2 * (N – 2)! = 2 (N – 1)! So the number of ways N people can be arranged in a straight line if 2 particular people must be separated = N!

How many ways can 3 people be arranged in a line?

Suppose we have three people named A, B, and C. We have already determined that they can be seated in a straight line in 3! or 6 ways. Our next problem is to see how many ways these people can be seated in a circle.

How many ways may these same people line up if two of the people refuse 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.

What is the number of ways to arrange 5 objects?

120 ways
So we say that there are 5 factorial = 5! = 5x4x3x2x1 = 120 ways to arrange five objects.

How many ways can 6 students be arranged in a line at the door?

EXAMPLE 2: How many ways can you line up 6 students? 720. There are 6 choices for the first position, 5 for the second, 4 for the third, 3 for the fourth, 2 for the fifth, and 1 for the sixth.

How many different ways can 12 people be arranged?

If not, we have possible ways. Add the together, and we get 479,001,600 possible combinations.

How many ways are possible if 3 persons insist on following each other?

3! = (24)(6) = 144 different ways.

How many ways can 5 people?

Answer: If the symmetry of the table is not taken into account the number of possibilities is 5! = 120. In this case it would be the same as ordering people on a line. However if rotation symmetry is taken into account, there are five ways for people to sit at the table which are just rotations of each other.

How many ways can 5 people line up at a checkout?

So the total number of different orderings for the 1st, 2nd and 3rd people combined would be 5*4*3 = 60.

How many ways can two children be arranged in a set?

Out of the total arrangement, we know that two particular children when together can be arranged in 240 ways. Therefore, total arrangement of children in which two particular children are never together will be 720 – 240 ways, i.e. 480 ways. Example 2:Consider a set having 5 elements a,b,c,d,e.

Is there any other way to arrange the elements of set?

As you can see, there are no other ways to arrange the elements of set A. In permutation, the elements should be arranged in a particular order whereas in combination the order of elements does not matter. Also, read: Permutation And Combination

How to find the number of possible permutations?

In other words, the permutation is considered as an ordered combination. P (n,r) = n!/ (n-r)! Let us understand all the cases of permutation in details. If n is a positive integer and r is a whole number, such that r < n, then P (n, r) represents the number of all possible arrangements or permutations of n distinct objects taken r at a time.