Permutations Examples on Order1

In this class, We discuss Permutations Examples on Order1.

The reader should have prior knowledge of permutations and combinations basics. Click Here.

Example:

Given three characters X, Y, and Z.

We need to find the total permutations possible which contain X before Y.

Solution:

The total permutations are given below.

X, Y, Z

X, Z, Y

Z, X, Y

Z, Y, X

Y, X, Z

Y, Z, X

The first three possibilities are having X before Y.

X, Z, Y is the case we need to understand.

X before Y means in between X and Y we can have other characters.

To solve these types of examples. We do selection first.

Total three characters. We need to select two positions from three positions.

Selections can be done in 3c2 ways.

Fix X and Y, and then the remaining positions can be filled with the remaining characters.

The below diagram shows the permutations.

3c2 * 1! is the total permutations.

Example:

Take the word “examply.”

Permutations that contain vowels in ascending order.

Solution:

Total seven elements.

Two vowels a,e.

Selection of two positions from seven positions is done in 7c2 ways.

The remaining five positions are filled in 5! Ways.

Total 7c2 * 5! ways.

Example:

Take the word “permutation.”

Find all arrangements containing vowels in ascending order.

Solution:

Total 11 elements.

Five vowels: a, e, i, o, u.

Selecting five positions out of eleven positions is 11c5 ways.

The remaining positions are filled with other characters.

“t” is repeated twice.

Total possibilities are 11c5 * 7!/2!