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How many different words can be formed by jumbling the letters in the word MISSISSIPPI in which no two S are adjacent?

How many different words can be formed by jumbling the letters in the word MISSISSIPPI in which no two S are adjacent?

Grade:upto college level

5 Answers

Latika Leekha
askIITians Faculty 165 Points
9 years ago
We have the word MISSISSIPPI
In this word there are 4 I’s, 4 S’s, 2 P’s and 1 M.
No two S should be together, hence we can place S at these places
_ M _ I _ I _ I _ I _ P _ P _ .
Therefore, the possible number of words is given by 8C4 . 7! / 4!2!.
= 8C4 . 7 .6! / 4. 2!
= 7. 8C4 . 6C4
This is the required answer.
Thanks & Regards
Latika Leekha
askIITians Faculty
Samar Zaidi
15 Points
6 years ago
After 4 she forgot to add "!"It should be 6!/(4!2!). But her explanation was perfect. Because of this it become difficult to understand the problem
Manoj gupta
54 Points
6 years ago
You have not arrange S`s because we have to arrange s also bug all of your explanation is perfect so please correct it if I am wrong them tell me the reason
Pragyanam Dubey
9 Points
5 years ago
Their is no need to arrange  S's as they are identical.even if u have to arrange by multiplying by 8! then u must have to divide by 8! As all S are identical
Yash Chourasiya
askIITians Faculty 256 Points
3 years ago
Dear Student

The given word isMISSISSIPPI
In this word there are 4 I’s, 4 S’s, 2 P’s and 1 M.
Other thanS, seven lettersM,I,I,I,P,P,Ican be arranged in (4!*7!)/2! ​=3.7C4​
Now, fourScan be placed in8spaces in the 8C4​ways.
Desired number of ways=3.7C4​.8C4​

I hope this answer will help you.
Thanks & Regards
Yash Chourasiya

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