# If the letters of the word KRISNA are arranged in all possible ways and these words are written out as in a dictionary,

**Question:**

If the letters of the word KRISNA are arranged in all possible ways and these words are written out as in a dictionary, then the rank of the word KRISNA is

(a) 324

(b) 341

(c) 359

(d) none of these

**Solution:**

(a) 324

When arranged alphabetically, the letters of the word KRISNA are A, I, K, N, R and S.

Number of words that will be formed with A as the first letter = Number of arrangements of the remaining 5 letters

= 5

Number of words that will be formed with I as the first letter = Number of arrangements of the remaining 5 letters

= 5!

∴ The number of words beginning with KA = Number of arrangements of the remaining 4 letters

= 4!

The number of words starting with KI = Number of arrangements of the remaining 4 letters

= 4!

The number of words starting with KN = Number of arrangements of the remaining 4 letters

= 4!

Alphabetically, the next letter will be KR.

Number of words starting with KR followed by A, i.e. KRA = Number of arrangements of the remaining 3 letters

= 3!

Number of words starting with KRI followed by A, i.e. KRIA = Number of arrangements of the remaining 2 letters

= 2!

Number of words starting with KRI followed by N, i.e. KRIN = Number of arrangements of the remaining 2 letters

= 2!

The first word beginning with KRIS is the word KRISAN and the next word is KRISNA.

∴ Rank of the word KRISNA = 5! + 5! + 4! + 4! + 4! + 3! + 2! + 2! + 2

= 324