1
$\begingroup$

The question is in how many ways can 5 letters be mailed if there are 2 mail boxes available? I would say that there are 2 ways to put the first letter (either to Box 1 or Box 2) and there are also 2 ways to put the second letter, etc. so the total number of ways is $2^{5}=32$ but my textbook says the answer is $25$ which is $5^{2}$, the other way round. Who is right?

EDIT: Maybe their answer $25$ does not come from $5^{2}$ but $2^{5}-7$ and I simply forgot to subtract some extraneous ways?

$\endgroup$
6
  • $\begingroup$ This should be $2^5=32$, where the extraneous case come from! $\endgroup$ – user249332 Dec 14 '15 at 15:13
  • $\begingroup$ Sorry but I don't get what you mean. $\endgroup$ – Richard Smith Dec 14 '15 at 15:36
  • $\begingroup$ The answer is purely $2^5=32$, in this process, there is no over-counting. So, you need not subtract anything (unless there are some restrictions assigned, that you missed to mention). $\endgroup$ – user249332 Dec 14 '15 at 15:48
  • $\begingroup$ Ah, ok, thanks. $\endgroup$ – Richard Smith Dec 14 '15 at 16:05
  • $\begingroup$ Textbooks do have the occasional typo. Maybe someone forgot to put the "^" in "2^5." $\endgroup$ – Barry Cipra Dec 14 '15 at 17:45
2
$\begingroup$

The first letter can be posted in any of the $2$ post boxes. Therefore, it has $2$ choices.

Similarly, the second, the third, the fourth and the fifth letter can each be posted in any of the $2$ post boxes.

Therefore, the total number of ways the $5$ letters can be posted in $2$ boxes is $\color{red}{ 2\times 2\times 2\times 2\times 2=32}.$

$\endgroup$

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.