How would you approach a problem like this?
If I were to make words of length 5 from the first 10 letters it would be 10^5 or 10x10x10x10x10, right?
But how do I account for the repetition part? repeated does not mean that they have to be next to each other. It just means that the same letter exists more than once.
How many words/strings of length 5 can we make using the first 10 letters of the alphabet with at least one repeated letter
combinatorics-on-wordsdiscrete mathematicspermutations
Best Answer
First 10 alphabets of English language are :
A,B,C,D,E,F,G,H,I,J.
So, if you want to write the 5 letter string without any repetition, then, the ways should be : $$\binom{10}{5}*5!$$ Also, atleat 1 means : TOTAL WAYS(can repeat) - NONE REPEATING.
Thus, Total ways = $10*10*10*10*10 = 10^5$
Thus, required number of ways is: $$10^5 - \binom{10}{5}*5!$$
And that's your answer!