1
$\begingroup$

How many arrangements of $MATHEMATICAL$ are there in which $ME$ appear together but the $ME$ is not immediately followed by an $A$? (no MEA)

The answer is $(11!)/(3!2!) - (10!)/(2!2!)$

I am confused as to how this is the answer. There are 12 letters in $MATHEMATICAL$. I also don't understand the denominators. Is the first for the combinations of MEA and ME and the second is just ME and ME? There are $2$ M's and $1$ E.

$\endgroup$
4
$\begingroup$

Gluing the ME together as a single "character" yields 11 characters, with 3 repeated As and two repeated Ts. If we glue MEA together asa single character, we get 10 characters in total, two repeated As, and two repeated Ts. The difference of these numbers counts the strings with ME together, but not with MEAs. This is the answer that you have provided.

$\endgroup$

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.