Question

Ask for my friend, I don't know this either.

In how many ways can 5 letters be mailed if there are:
a) 2 mailboxes available
b) 4 mailboxes available

Edit: I erroneously wrote that 5 mailboxes is available in b).

Answer 1

My intuition is that the answer to the first one is 6 as:
A B
0 5
1 4
2 3
3 2
4 1
5 0

But the answer is 25. Apparently the letters are distinguishable.

Answer 2

@Kainui HELP!!!!!!

Answer 3

If the letters are distinguishable then each letter has 2 possible states : {box1, box2}
So total possible states for sending 5 letters would be : 2*2*2*2*2 = 2^5

Answer 4

if the letters are distinguishable I get 32 ways, not 25

Answer 5

thats for part a

Answer 6

Me too. I am so confused right now.

Answer 7

The answer to part a is 25 and part b is 625 = 25*25.

Answer 8

The book could well be wrong. It happened before but I need a solid answer to say the book is wrong.

Answer 9

Is it possible that the mail is indistinguishable but some mail can be lost in post? LOL!

Answer 10

list them all if that states arguement doesn't look solid

Answer 11

call the letters : l1, l2, l3, l4, l5

and boxes : b1, b2

Answer 12

It is basically
\[
\sum_{k=0}^5\binom{5}{k}=2^5
\]

Answer 13

thats the total number of ways of choosing 0->5 letters for first box

second box is determined after that so yeah

Answer 14

How do you deal with the second part though? 4^5?

Answer 15

Yes assuming the letters are distinguishable

Answer 16

If they're not distinguishable then the answer is simply 6 for part a and 56 for part b

Answer 17

oh, it looks like the answer is doing
(# of letters)^(# of boxes)
so 5^2 = 25
and 5^4= 625

Answer 18

The book is dumb?
\[
2^5=32\\
5^2=25\quad\text{book's answer to part a}\\
4^5=1024\\
5^4=625\quad\text{book's answer to part b}
\]

Answer 19

so the book is pretty close

Answer 20

the author must be drunk when writing solution

Answer 21

*facepalm*

I wouldn't call that pretty close.

Yes the author must be drunk.

Answer 22

It is beyond words!

Answer 23

they used both numbers, and an exponent.

Answer 24

whats the complete question anyways

Answer 25

That is the exact wording of that question LOL!

Answer 26

I know the question is worded poorly and it is pretty common in this textbook.

Answer 27

im just wondering if there is a way to get to textbook answer by putting constraints like

1) making letters indistinguishable
2) each box must have atleast 1 letter etc..

Answer 28

If those constraints are true, then part a would be 4 not 25.