Question

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

Answer 1

8!/(4!)(2!)

Answer 2

Could you please explain abhimanyu?

Answer 3

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!)

Answer 4

THANKS!!!

Answer 5

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?

Answer 6

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

Answer 7

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

Answer 8

so, no permutation for the S group.

Answer 9

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

Answer 10

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

Answer 11

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

Answer 12

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

Answer 13

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

Answer 14

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