Grade upto college level Algebra

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

aditya kashyap

12 Years agoGrade upto college level

5 Answers

Latika Leekha

12 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. ⁸C_{4 .}⁶C₄

This is the required answer.

Thanks & Regards

Latika Leekha

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Samar Zaidi

9 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

8 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

7 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

6 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 ⁸C₄ways.
Desired number of ways=3.⁷C₄.⁸C₄

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