Permutation Examples Rank of the Word

In this class, We discuss Permutation Examples Rank of the Word.

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Examples:

Rank of the word “kite”.

First, arrange them in ascending order.

e, i, k, t.

Find a number of words starting with e.

The number of words starting with e is 3! ways.

6 words possible.

Similarly, we can place “i” in the first position.

The remaining three positions are filled with the remaining three characters in 3! ways.

6 words possible.

Similarly, we can place “k” in the first position.

From ascending order, the second position should be filled with e.

The remaining two positions are filled with two characters using 2! ways.

The second position can now filled with “i”.

The next character is in ascending order.

The third position can be filled with “e.”

The last position is filled in 1! way.

The next word we get is “kite.”

Before we get the word kite, we have a total of 3! + 3! + 2! + 1! words possible.

So, the rank of the word kite is 16.

Example 2:

Take the word “take”.

The characters in ascending order are a, e, k, and t.

Starting with “a”, we have 6 words possible.

Starting with “e”, we have 6 words possible.

Starting with k, we have 6 words possible.

The next word we get is taek.

Finally, we get the word “take”.

The rank of the word “take” is 20.