The rank of the word SUCCESS, If all possible permutations of the word SUCCESS are arranged in dictionary order is - (a) 331 (b) 341 (c) 351 (d) 361

By Ritesh|Updated : November 14th, 2022

The rank of the word SUCCESS, If all possible permutations of the word SUCCESS are arranged in dictionary order is 331. The alphabetic letters in Success are S, U, C, and E.

Their dictionary order is C, U, S, E:

The number of words that are starting with C (C _ _ _ _ _ _) (no two C will be repeated but here we have three S) is 6!/3!.

The number of words that are starting with E (E _ _ _ _ _ _) (here we have two C and three S) is 6!/2!3!.

Now we want the word to start with S.

So, the number of words that are starting with SC (SC _ _ _ _ _) (here we have a single C and two S) is 5!/2!

The number of words that are starting with SE (SE _ _ _ _ _) (here we have two C and two S) is 5!/ 2! 2!

The number of words that are starting with SS (SS _ _ _ _ _) (here we have two C and single S) is 5!/2!

Now next word will be SUCCESS:

Now rank of the word SUCCESS is:

6!/3! + 6!/2! 3! + 5!/2! + 5!/2! 2! + 5!/2! + 1

= 120 + 60 + 60 + 30 + 60 + 1

= 331

Summary:

The rank of the word SUCCESS, If all possible permutations of the word SUCCESS are arranged in dictionary order is - (a) 331(b) 341(c) 351(d) 361

If all conceivable permutations of the word SUCCESS were ranked according to the dictionary, the word would come in at position 331. The act of placing all the components of a set into a certain sequence or order is known as permutation in mathematics.

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