1
$\begingroup$

The question is simple. A couple want to name their baby in such a way that his initials are in alphabetical order, with no repetition.The monogram is of the form ABC, where A is the initial of his first name, B his second name and C his last name.

My reasoning is simple. I realised that it's equivalent to picking up $3$ elements from a list of $26$ elements. We don't have to worry about counting if they're in alphabetical order because every $3$ tuple chosen like this will have one and only one alphabetical order. In other words, there is a one to one correspondence in between the number of ways of choosing $3$elements and the number of ways of arranging these $3$ elements in alphabetical order.

My answer is $$\binom{26}{3}$$

However, it is wrong. What is the mistake here ?

Edit : I left out the name of the couple because I didn't think it mattered. Their name was Mr. And Mrs. Zeta. Now, I see why the answer makes sense. The baby shares the parents last name and the remaining two alphabets can be chosen in $\binom{25}{2}$ ways, each of which correspond with only one alphabetical arrangement since they are all different combinations.

$\endgroup$
  • $\begingroup$ The answer is indeed $\binom{26}{3}$. Clearly described reasoning. $\endgroup$ – André Nicolas Feb 25 '16 at 5:21
  • $\begingroup$ Why do you claim it is wrong? $\endgroup$ – Eric Towers Feb 25 '16 at 5:23
  • $\begingroup$ The book gives the answer as $\binom{25}{2}$ $\endgroup$ – user230452 Feb 25 '16 at 5:26
2
$\begingroup$

Depends. What's the couple's last name? (Or are you saying the child will not share the parents' last name?)

$\endgroup$
  • $\begingroup$ Wow. That was brilliant. Their last name was Zeta, but I didn't think it mattered until you said it. $\endgroup$ – user230452 Feb 25 '16 at 5:27
  • $\begingroup$ Now, I see why it is $\binom{25}{2}$. $\endgroup$ – user230452 Feb 25 '16 at 5:28

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.