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5 Min Read

A very common type of question that gets asked in various banking and management entrance exams is based upon the concept of finding out the rank of a word. In this post, I will like to discuss the concept behind the same. Let us look at the two types.

Suppose that you are given a word in which none of the letters are repeated and you asked to find out the rank of the word in a dictionary. For example, if the word which was given to you was CAT, it will be very easy to find out its rank. You will write down all possible combinations of the letters. Those are:

CAT,CTA, ATC, TCA, ACT, TAC

Now, you will arrange them in alphabetical order. It would become something like this:

ACT, ATC, CAT, CTA, TAC, TCA

CAT is third in the above list. So, the rank of the word CAT is 3.

But, as you might have realized by now – the problem would become extremely difficult if the word is bigger. Let us say that the word is Ganesh.

With just 6 letters, total possible arrangements are 6! or 720. It is not practical to write all of them down and find out the rank of the word Ganesh .

To solve questions like these, here is the process we need to follow.

**Step 1: Write down the letters in alphabetical order.**

The correct order will be A ,E ,G ,H ,N and S Rank them as alphabetical order

**Step 2: Find out the number of letters on the right with lower rank ** As G is 3 letter in alphabetical order and there are 2 letters on the right side with lower rand than G so we write 2 as its value and A is ranked 1 and there is no letter on right side of A which is lower rank than A so value is 0

**Step 3: Write 0! from right end and continue till left end with increasing order **

Such as we start with 0! and reached 5! for first value.

**Step 4: Multiply with respective value and get the answer.**

**240 + 0 + 12 + 0 + 2 + 0 =254**

Word | G | A | N | E | S | H |

ALPHABETICAL ORDER | 3 | 1 | 5 | 2 | 6 | 4 |

RANKING ON RIGHT LOWER THAN CURRENT |
2 | 0 | 2 | 0 | 2 | 1 |

POSITION OF FACTORIAL | 5! | 4! | 3! | 2! | 1! | 0! |

TOTAL RANK | 240 | 0 | 12 | 0 | 2 | 0 |

**jitesh Gupta**

**HEAD MENTOR AT HEADACHE TUTORIALS **

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