Answer to Question #224709 in Discrete Mathematics for Syed Mohammad Zaid

Question

Suppose the city of MISSISSAUGA has a contest where they arrange the letters of their city name in a particular order. The city residents have to guess which order the city has chosen, and the winner gets $10 000. The rules allow people to submit more than one entry, but they each have to be mailed individually. A friend of yours wants to mail every possible entry to be guaranteed to win the $10 000. Use a mathematical argument to explain to your friend why this isn’t a good idea. Include evidence of your work by typing out your full solution.

Answer 1

There are $4\ S's, 2\ I's, 2\ A's$ in MISSISSAUGA.

There are

$$\dfrac{11!}{4!2!2!}=415800$$

possible arrangements for the letters in MISSISSAUGA.

At $\$0.96$ per envelope to mail ($85$ cents plus tax), it would cost

$$415800\times\$0.96=\$399168$$

to send in every possible entry, which is much more than the $10000 prize.