If all the letters of the word coach are rearranged in all possible ways and awards does formed are arranged as in a dictionary then the rank of the word coach will be?

Question

Answer

Rank of the word 'coach' when all letters are rearranged

Permutation of letters in the word 'coach'

The word 'coach' has five letters and we need to find all possible permutations of these letters. To do this, we can use the formula for permutations of n objects taken r at a time, which is n!/(n-r)!. In this case, we have n=5 and r=5, so the number of permutations is:

5!/(5-5)! = 5! = 120

So there are 120 possible arrangements of the letters in the word 'coach'.

Arranging the permutations in a dictionary

To find the rank of the word 'coach' in this list of permutations, we need to arrange them in alphabetical order. We can do this by starting with the first letter of each permutation and comparing them. If they are the same, we move on to the second letter, and so on, until we find a difference. The permutation with the earlier letter at that position comes first in the dictionary.

For example, the first few permutations in alphabetical order are:

- achoC
- acoCh
- acCho
- acCoH
- acHco
- acHoC
- acocH
- acoHc
- accho
- accoH
- acocC
- acohC
- acooc
- acooC
- acHoc
- acHco

We can continue this process until we reach the permutation 'coach', which is the 24th permutation in alphabetical order.

Rank of the word 'coach'

Therefore, the rank of the word 'coach' when all letters are rearranged and the words are arranged in a dictionary is 24.

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