How many different 5-letter strings can be formed using the letters from the word ABRACADABRA if duplicated letters are allowed but no letter can be used more times than it occurs in the word?
Though this seems like a duplicate, there is a nuance in my question in which i am about to explain:
According to an answer key it is 1271 because
if we set the variables vwxyz, there are 5! ways, which i understand, but
if there is a repeated letter
vvxyz, then there are $3*4*(5!/2!)$ many ways and so on and so forth, But why is it $3*4*(5!/2!)$ ? why do you multiply the 4 and the 3?
I was wondering that there are 5 ! configurations with 2! repeated letters so wouldnt that just be $\frac{5!}{2!}?$