IMO D
first letter can be posted in any of the 3 boxes - 3
2nd----------------------------------------------- 3
3rd----------------------------------------------- 3
4th------------------------------------------------3
5th------------------------------------------------3
total = 3*3*3*3*3 = 3^5

I always get confused between the value of 'n' and 'r' in n^r. I went for 5^3.
Is there a easier way to avoid this confusion?

I always get confused between the value of 'n' and 'r' in n^r. I went for 5^3.
Is there a easier way to avoid this confusion?

well write in proper form.
1st letter -3 ways
2nd - 3 ways
3rd - 3ways
4th-3 ways
5th-3 ways
thus 3*3*3*3*3 = 3^5 (this way you won't go for 5^3)

3^5 is the correct answer.thanks cans for the explanation

I need to confirm 1 query -
Is it that in this question you have also given importance to the order in which the letter have been posted. As in, have you assumed that letters posted in this format (Letters 1 and 2 in 1st post box, letters 3 and 4 in 2nd post box and letter 5 in 3rd post box) is other than letter posted in this format(Letters 3 and 4 in 1st post box, letters 1 and 2 in 2nd post box and letter 5 in 3rd post box).
Please help!

vinitrathi1 wrote:I need to confirm 1 query -
Is it that in this question you have also given importance to the order in which the letter have been posted. As in, have you assumed that letters posted in this format (Letters 1 and 2 in 1st post box, letters 3 and 4 in 2nd post box and letter 5 in 3rd post box) is other than letter posted in this format(Letters 3 and 4 in 1st post box, letters 1 and 2 in 2nd post box and letter 5 in 3rd post box).
Please help!

The letters can be in any order. (they are not numbered. I just said 1st,2nd letter to distinguish them.)
and yes I assumed the above two cases you mentioned as different.

Thanks for your help, I really appreciate!
Can I ask you another question? What really compels you to assume that they are different? (I assume that it is also not implied in the question)

if all of them were identical, it would have been mentioned in the question
like: 5 identical letters were posted....

cool.thanks a lot!

Just curious, what would the answer be if the question was:
Q.In how many ways can 5 identical letters be posted in 3 post boxes, if any number of letters can be posted in all of the three post boxes?

vinitrathi1 wrote:Just curious, what would the answer be if the question was:
Q.In how many ways can 5 identical letters be posted in 3 post boxes, if any number of letters can be posted in all of the three post boxes?

let A,B,C order in which letters are on boxes
5,0,0 = 3!/2! =3
4,0,1 = 3! =6
3,1,1 =3!/2! = 3
3,0,2 = 3! = 6
2,2,1= 3!/2! =3
total = 21