Question 638033
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Mr. and Mrs. Richardson want to name their new daughter so that her initials (first, middle, and last) will be in 
alphabetical order with no repeated initial. How many such triples of initials can occur under these circumstances?
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The last name of the newborn child should be Richardson, so the last letter of the triple must be R.


English alphabet has 26 letters, and 'R' is the 18-th letter in the English alphabet.


So, all possible triples are of the form  ABR,  where A and B are two different letters 
of the English alphabet preceding 18-th letter 'R'.


For this pair (AB) in the alphabetical order,  there are  {{{(17*16)/2}}} = 8*17 = 136 possible different opportunities.


Hence, 136 triples of initials can be formed, as parents Mr. and Mrs. Richardson wish.    <<<---===  <U>ANSWER</U>
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Solved.