Permutation Examples Rank of the Word1

In this class, We discuss Permutation Examples Rank of the Word1.

The reader should have prior knowledge of the rank of the word simple example. Click Here.

In our last class example, we took the word and found the rank of the word.

In this example we take the rank and find the word possible at the rank.

Example:

Given a, d, k, k, p, and t.

Find the word that contains rank 170.

Solution:

The first position is filled with a.

The number of possible words with the initial character a is 5!/2!

Sixty words are possible with the character “a”.

Similarly, starting with “d”, 60 words is possible.

Starting with “k”, we have 120 words possible.

Starting with “k” we are moving beyond the rank 170.

The first two positions are considered “k and a”.

With “k and a”, the total number of words possible is 4! i.e. 24 words.

To now, we have a total of 144 words.

Similarly, starting with “k and d”, we have 24 words possible.

144 + 24 = 168

The 169th word is kkadpt.

The 170th word is kkadtp