Permutain and combination

Question

Hi, 

Help me with the solution of this problem

In how many ways can 5 letters be posted in 3 post boxes, if any number of letters can be posted in all of the three post boxes?

A. 5 C 3

B. 5 P 3

C. 53

D. 35

E. 25

Thanks

BG · Answer

You can drop the first letter in 3 ways , the second in 3 ways and so on up to the fifth. Then you will have 3x3x3x3x3 or 3^5 which is 243

qpoo · Answer

it is not clear in the question:
1) can the letters be reused from box1 to box2
 if that is the case, none of the choices is correct
2) assume no same letter on two boxes, and at least one letter has to
 be on one box
 You can put 1 letter each on 2 boxes, the third box with 3 letters
 there are: 5x4 ways
 You can also put 1 letter on 1 box, 2 letters on the other two boxes each
 there are: 5x4x3/2 ways

ranga41 · Answer

Assumption all letters are identical 

there are six different cases

All 5 letters posted

5+0+0 (3 ways)
4+1+0 (6 ways)
3+2+0 (6 ways)
3+1+1 (3 ways)
2+2+1 (3 ways)

only 4 letters are posted

4+0+0 (3 ways)
3+1+0 (6 ways)
2+2+0 (3 ways)

only 3 letters posted

3+0+0 (3 ways)
2+1+0 (6 ways)

only 2 letters posted

2+0+0 (3 ways)
1+1+0 (3 ways)

only 1 letter posted

1+0+0 (3 ways)

no letters posted

0+0+0 (1 way)

Adding all up i get  52  ways....I will go with 53 i dont know where i am missing 1 possibility or if i am wrong....

duttsit · Answer

each letter can be posted into ANY post box.
1st letter has 3 options
2nd letter has 3 options..so on

total ways = 3 ^ 5

No idea, why ans choices doesnt include this.

Permutain and combination

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