# Math Help - combination/permutation

1. ## combination/permutation

I've done this before like months ago and now I forgot what these mean, so I need someone to explain to me what's going on lol

Question: How many different 4 letters words can be formed using letters of the word "MISSISSIPPI"

4 same --- 2 ways
3 same 1 different --- 2C1 X 3C1 X4!/3! <<I need someone to explain each of them to me ,3 of those ,if the other 3 at bottom are different ,please explain too thanks!
2 same 2 same --- 3C2 X4!/2!
2 same 1 diff 1 diff --- 3C1 X 3C2 4!/2!
1d 1d 1d 1d --- 4!

Total:176

2. ## Re: combination/permutation

Originally Posted by wong93
I've done this before like months ago and now I forgot what these mean, so I need someone to explain to me what's going on lol

Question: How many different 4 letters words can be formed using letters of the word "MISSISSIPPI"

4 same --- 2 ways
3 same 1 different --- 2C1 X 3C1 X4!/3! <<I need someone to explain each of them to me ,3 of those ,if the other 3 at bottom are different ,please explain too thanks!
2 same 2 same --- 3C2 X4!/2!
2 same 1 diff 1 diff --- 3C1 X 3C2 4!/2!
1d 1d 1d 1d --- 4!

Total:176
The explanation takes you through how to form 4 letter words with the different possibilities. There are 4 different letters.
• There are 2 ways to have a four letter word with the same letters (SSSS, IIII).
• 3 same letters is ${2 \choose 1}$ and 1 different letter is ${3 \choose 1}$ since there are 3 letters different from the same letters. The multiplier $\frac{4!}{3!}=4$ takes care of the fact that you could have 4 arrangements as in SSSP, SSPS, SPSS, PSSS.
• 2 same letters is ${3 \choose 2}$(i.e. there are three different letters that you can have two of). Again, the $\frac{4!}{2!}$ is a multiplier to include the arragements
• Can you continue with this logic to understand the rest?

Hope this helped.

3. ## Re: combination/permutation

the questions stated that 4 letters word only and i don't need answer for this question ,i need explanation of what is being written there,cause i forgot what are those,thanks anyway