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## Homework Statement

How many ways are there to arrange the letters of the word VISITING with no pairof consecutive I's?

## Homework Equations

C(n,k) P(n,k)

## The Attempt at a Solution

I am calculating the entire number of arrangements possible at P(8,5). I then want to find out the entire number of cases where there are at least two I's consecutively placed, and subract that from P(8,5).

Since there are eight places to put letters, there are seven possible ways to places to I's consecutively. What I am unsure of is if those seven arrangements of letters include the six possible cases where all three I's are consecutively placed.