<p>A,B,C,D,E,F,G</p>
<p>A list consists of all possible three-letter arrangements formed by using the letters above such that the first letter is D and one of the remaining letters is A. If no letter is used more than once in an arrangement in the list and one three-letter arrangement is randomly selected from the list, what is the probability that the arrangement selected will be DCA? </p>
<p>You need to find the total # of three-letter arrangements w/ first letter D and one of the remaining letters is A.</p>
<p>The first letter is fixed; forget about it. Then we pick A and one other letter. There are five possible choices for the third letter (it cannot be A or D), and for each choice we have two arrangements (DA* or D*A where * is the third letter) so there are 10 rearrangements to pick from. Since only one of them is DCA, the probability is 1/10.</p>
<p>Thanks!!</p>