The question is how many ways the word INDIA can be re-written.
I N D I A
There are 5 letters in this word. The letter I is repeated twice, and this number doesn't make any sense if there positions are interchanged.
So,basically the number of ways INDIA can be arrange consider there are two types of I --- the answer is factorial 5. However the letter 'I' is repeated twice. Thus, we should subtract the number of ways the the two letter I is occurred. Thus, we should subtract it. However, we always divide it --- 5!/2. I want to understand, whey do we do so? Why do we divide by 2 here rather than doing subtraction? I couldn't get the logic here. Can someone please explain to me?