PrepRung
Sign inSign up free

NDA 2016 Maths · Mathematics · Permutations and Combinations · hard

The number of distinct arrangements of all the letters of the word MISSISSIPPI is

Single correct option

The number of distinct arrangements of all the letters of the word MISSISSIPPI is
  1. A. 6930069300
  2. B. 207900207900
  3. C. 3465034650
  4. D. 1732517325
Show answer and solution

Answer: (C) 3465034650

There are 11 letters: I appears 4 times, S 4 times, P 2 times and M once. The number of arrangements is 11!4! 4! 2!=34650\dfrac{11!}{4!\,4!\,2!}=34650. Dividing by only 4! 4!4!\,4! (ignoring the repeated P) gives 69300, and over-dividing by an extra 2!2! gives 17325.
Report a mistake

Original question written in the NDA 2016 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake