Question 1172924
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(1) The name has 14 letters, including 3 of one letter and 2 each of two other letters.  By a well known counting principle, the number of distinct arrangements is<br>
{{{14!/((3!)(2!)(2!))}}}<br>
(2) To find the number of distinct arrangements with the two L's together, simply treat the two L's as a single "letter"; that gives 13 letters with 3 of one letter and 2 of another; the number of distinct arrangements is<br>
{{{13!/((3!)(2!))}}}<br>
(3) There is only distinct arrangement in which all the letters are in alphabetical order.<br>