Question

Total number of words formed by the letters of the word 'MISSISSIPPI' in which any two S are separated is equal to:
A) 7350
B) 6300
C) 12600
D) 5000

Answer 1

Hint: A permutation is an arrangement of all or part of a set of objects, with regard to the order of the arrangement, and formula for total arrangement is \[\dfrac{{n!}}{{\left( {p! \times q! \times r!} \right)}}\]. Using this formula, multiple types of questions related to permutation can be solved. One could say it is an ordered combination.

Complete step-by-step answer:
There are 11 letters in the word “MISSISSIPPI”.
Here, We have 4 I's, 4 S's , 2P's & 1 M.
Given in the question that no two S should be together, which we can place S at there places,
_M_I_I_I_I_P_P_
So there are 8 places in which we have to place 4 S’s
Therefore, the possible No. of words of given by,
= \[\dfrac{{{}^8{C_4} \times 7!}}{{4!2!}} \\
7!=7*6*5*4*3*2*1\\
4!=4*3*2*1\\
2!=2*1\\
{}^8{C_4}= \dfrac{{8!}}{{4!4!}}\\
= 7350{\text{ ways}}\]

Note: A permutation or combination is a set of ordered things. The “things” can be anything at all: a list of planets, a set of numbers, or a grocery list.Combination: If you don’t care what order you have things, it’s a combination. Think of combining ingredients, or musical chords: Flour, salt and water in a bowl is the same as salt, water and flour. Lottery tickets, where you pick a few numbers, are a combination. That’s because the order doesn’t matter (but the numbers you select do).Permutation: If you care about order, it’s a permutation. Picking winners for a first, second and third place raffle is a permutation, because the order matters. Permutation isn’t a word you use in everyday language.