When we want to arrange a group of items in which some of the items are identical, we can use something called the MISSISSIPPI rule. It goes like this:nahid078 wrote:How many different strings of letters can be made by reordering of the word SUCCESS?
If there are n objects where A of them are alike, another B of them are alike, another C of them are alike, and so on, then the total number of possible arrangements = n!/[(A!)(B!)(C!)....]
So, for example, we can calculate the number of arrangements of the letters in MISSISSIPPI as follows:
There are 11 letters in total
There are 4 identical I's
There are 4 identical S's
There are 2 identical P's
So, the total number of possible arrangements = 11!/[(4!)(4!)(2!)]
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In SUCCESS:
There are 7 letters in total
There are 2 identical C's
There are 3 identical S's
So, the total number of possible arrangements = 7!/[(2!)(3!)]
= 420
Cheers,
Brent
