Permutations of indistinguishable items

I’ll give the most common example.

the ways to arrange the letters of the word MISSISSIPPI is equal to
image

But what if we are asked to select and arrange, say, 5 of the letters from the word MISSISSIPPI?

Also, what if we are asked to find way to choose, say, 5 letters from the word MISSISSIPI? Is there a formula for indistinguishable items for combinations as well?

No formula ,at-least to my knowledge! Probably you’ll have to break it down to smaller cases and then solve those. For eg: In-case of the word “MISSISSIPPI” we can make the following cases to choose 5 letters :

  • all 5 selected letters are different;
  • one letter appears twice and three other letters appear once;
  • one letter appears three times and two other letters appear once; and
  • two different letters each appear twice.

Then we can use combinations to calculate the number of ways each case can happen.