kevo 3 years ago How many ways are there to rearrange the letters in the word "MISSISSIPPI" so that the resulting word contains four consecutive letters S? Hint: Think of the string "SSSS" as a new letter

1. AbhimanyuPudi

8!/(4!)(2!)

2. kevo

Could you please explain abhimanyu?

3. AbhimanyuPudi

Take {S,S,S,S} to be one letter....then you will have 8letters in which there are 4I's and 2P's....So arranging n things in which m are one type and n are of one type is n!/(m!)(n!)

4. kevo

THANKS!!!

5. kevo

hold on though, wouldn't we need to factor in that the S's can be in any particular order, so we have to avoid multiples, yeah?

6. kevo

8!/(4!*4!*2!)?

7. Ishaan94

it won't matter. SSSS is gonna look the same.

8. Ishaan94

so, no permutation for the S group.

9. kevo

So I wouldn't have to take into account the S's? But for the I's and the P's?

10. Ishaan94

because you can have ISSSSI... or IISSSSI... but not SSIISS...

11. AbhimanyuPudi

IMISSSSIPPI and MSSSSIIPIPI are two of the arrangements...here if you take a look, you will find all S's together but I's and P's may be all together or a few together and others seprated or all may be separated...So, I's and P's must be considered for arranging but not S's

12. kevo

OH! I see where this is going. But couldn't you also have ISSSSI and ISSSSI with just the S's rearranged?

13. AbhimanyuPudi

if S's are rearranged the word looks the same but if I's and P's are rearranged, word changes and thats what the question is about..Find the different words formed by reaarrangement

14. kevo

Ahhhhh I see, thank you for your guys' help! I really appreciate it