Question 1203273
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The comment from tutor @ikleyn is correct.  In counting the number of arrangements with the two I's together, there is only one way to arrange those two I's, because they are the same letter.<br>
The total number of arrangements is of 11 letters including 2 pairs.  That number is {{{(11!)/((2!)(2!))}}}<br>
For the number of arrangements with the 2 I's together, treat them as a single unit.<br>
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NO!...  Then there are 10 items with one (other) pair; and the two I's in the unit can be arranged in either of 2 orders.  This number is then {{{(2)((10!)/(2!))}}}<br>
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Yes...  Then there are 10 items with one (other) pair.  the number of arrangements here is then {{{(10!)/(2!)}}}<br>
Subtract the second number from the first to get the number of arrangements in which the two I's are separated (i.e, not together).<br>
You can do the actual calculations....<br>