Permutations questions (Head Scratch)

[eddykay101]

Hi all, I have just started my journey into Data Science and was looking at practicing skills I have learnt. What did I do? I went on google and typed practice permutation problems and I came across this question.

Jimmy has the letters for the state of MISSISSIPPI written on cards, one letter per card. He turns the cards over and mixes up the order. If he selects one card at a time without replacing the cards, what is the probability that he will spell the word MISS in order?

Apparently the correct answer is 1/165 But I am trying to understand how that is. And was wondering if any of you math geniuses could help me please.

 

[Cubist]

It seems that you want to solve this problem using permutations. I've done this, and I think their answer is correct!

Hint: How many permutations of MISSISSIPPI are there, and how many of them begin with MISS. Do you know how to answer the first part of this hint? Please post back with your work/ ideas so that we can guide you.

 

[pka]

Hi all, I have just started my journey into Data Science and was looking at practicing skills I have learnt. What did I do? I went on google and typed practice permutation problems and I came across this question.
Apparently the correct answer is 1/165 But I am trying to understand how that is. And was wondering if any of you math geniuses could help me please.

Please post a link to where you found this question. The answer depends upon how the question is read.
In it is read that the first four letters he turns over are [imath]MISS[/imath] in that order, then the answer is
[imath]\dfrac{\dfrac{7!}{(2!)^2(3!)}}{\dfrac{11!}{(4!)^2(2!)}}=\dfrac{1}{165}[/imath] SEE HERE
Thus we need the link to be sure how to read the question.

 

[Dr.Peterson]

I can see several ways to approach this, so we do need to see your work in order to tell you where you might be making a mistake. You may be closer than you think, even if your way is very different from any of ours.

One I found easy was to make the tiles distinct (e.g. consider them to be different colors, or put subscripts on identical letters), and then count the permutations of those distinct tiles that spell MISS in order (that is, how many ways are there to pick an M, then an I, then two S's).