Three of the letters of SPINS are randomly selected to form a word. How many different words are possible? These words do not have to be real words, for example, spn is one of the words.
1 Answer
33 "words"
Explanation:
This is a permutation problem where we care about the order of the letters. The general formula is:
If we were working with letters that are all unique, say with the word SPINE, we'd be picking 3 letters at a time from 5 letters in total, giving:
But we have SPINS - and so the second S is a duplicate.
To deal with this, we can break down the calculations into different situations. One is where we draw up to 1 S and the other is where we draw both.
Up to 1 S
This gives a population of 4 letters being drawn 3 at a time:
Both S's
We can put the letter that isn't an S into spots 1, 2, or 3, giving 3 choices. There are 3 letters that aren't S's. And so we have:
Total
