Number of words that can be formed from the letters of the word ENGINEER so that order of the vowels do not change?
My work : Since order of vowels does not change, the order should always be EIEE. So I assumed it to be a single object ( EIEE) and arranged it along with NGNR in $5!/2!$ ways. But in this case, the situation when first E is separated by rest IEE and many more like that are not included. So how do I involve all cases?
Best Answer
You should simply count the number of arrangements of the letters N-G-N-R among eight positions, i.e. $(8!/(4!4!))*(4!/2!)$.