Question

In how many ways 5 letters be posted in 3 post boxes,if any number of letters can be posted in all of the three post boxes??

Answer 1

first of all the 5 letters can be arranged in 5! ways or 120 ways

now let's place them in the boxes, assume that some

A B C
5 0 0
4 0 1
4 1 0
3 2 0
3 0 2
3 1 1
2 3 0
2 0 3
2 2 1
2 1 2
1 4 0
1 0 4
1 3 1
1 1 3
1 2 2
0 5 0
0 0 5
0 4 1
0 1 4
0 3 2
0 2 3 , I counted 21 of these, check this

number of ways = 120(21) = 2520

Answer 2

Answer should be 231.

Answer 3

Happy Sunday!
If you consider the letters first then you have
____ then ______ then _____ then _____ then _____
and each of the five letters can have three places to go
3 then 3 then 3 then 3 then 3
thus
3 x 3 x 3 x 3 x 3 = 243 possibilities
Did you have a typo when you wrote 231 at 9:04 this morning??
The correct answer is 243 : )