I'm not looking for a solution to a question, but rather an explanation for a solution.
Question 1: How many ways are there to arrange 12 identical apples and five different oranges in a row so that no two oranges will appear side by side?
The solution: C(13, 5) * 5!, but I don't understand why you have to multiply by 5!. In other words, why do you have to make the 5 oranges distinct?
Question 2: How many ways are there to arrange the letters in VISITING with no pair of consecutive Is?
The solution: C(6,3) * 5!, here 5! represents the arrangement of the non-I's. So why, unlike the first question, do you not need to make the I's distinct by multiplying 3!? Why is the answer not C(6, 3) * 5! * 3!?
What's so different about these 2 questions that you have to make the oranges distinct but not the I's?