Please help me with this sum

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vinitrathi1: Newbie | Next Rank: 10 Posts; Posts: 8; Joined: Sun Jun 05, 2011 2:34 pm; Thanked: 2 times

by vinitrathi1 » Sun Jun 05, 2011 2:45 pm

Q.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?

1. 5 C 3
2. 5 P 3
3. 5^3
4. 3^5
5. 2^5

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Source: Beat The GMAT — Problem Solving | Sun Jun 05, 2011 2:45 pm

cans: Legendary Member; Posts: 1309; Joined: Mon Apr 04, 2011 5:34 amFollowed by: 123 members; Location: India; Thanked: 310 times; GMAT Score:750

by cans » Sun Jun 05, 2011 4:03 pm

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

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Sun Jun 05, 2011 5:26 pm

vinitrathi1 wrote: 1. 5 C 3
2. 5 P 3

The solution that cans gave is great.

I only want to add that, on the GMAT, students aren't required to know the combination (nCr) and permutation (nPr) notation.

The answer choices will given as either numbers or expressions.

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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vzzai: Senior | Next Rank: 100 Posts; Posts: 85; Joined: Tue Sep 02, 2008 12:13 am; Thanked: 1 times; GMAT Score:650

by vzzai » Sun Jun 05, 2011 7:16 pm

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?

Thank you,
Vj

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cans: Legendary Member; Posts: 1309; Joined: Mon Apr 04, 2011 5:34 amFollowed by: 123 members; Location: India; Thanked: 310 times; GMAT Score:750

by cans » Sun Jun 05, 2011 8:38 pm

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)

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aftableo2006: Senior | Next Rank: 100 Posts; Posts: 99; Joined: Sat Oct 16, 2010 1:55 pm; Thanked: 1 times

by aftableo2006 » Sun Jun 05, 2011 11:03 pm

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

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vinitrathi1: Newbie | Next Rank: 10 Posts; Posts: 8; Joined: Sun Jun 05, 2011 2:34 pm; Thanked: 2 times

by vinitrathi1 » Mon Jun 06, 2011 6:03 am

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!

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cans: Legendary Member; Posts: 1309; Joined: Mon Apr 04, 2011 5:34 amFollowed by: 123 members; Location: India; Thanked: 310 times; GMAT Score:750

by cans » Mon Jun 06, 2011 6:30 am

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.

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vinitrathi1: Newbie | Next Rank: 10 Posts; Posts: 8; Joined: Sun Jun 05, 2011 2:34 pm; Thanked: 2 times

by vinitrathi1 » Mon Jun 06, 2011 1:13 pm

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)

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cans: Legendary Member; Posts: 1309; Joined: Mon Apr 04, 2011 5:34 amFollowed by: 123 members; Location: India; Thanked: 310 times; GMAT Score:750

by cans » Mon Jun 06, 2011 8:05 pm

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

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Cans!!

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vinitrathi1: Newbie | Next Rank: 10 Posts; Posts: 8; Joined: Sun Jun 05, 2011 2:34 pm; Thanked: 2 times

by vinitrathi1 » Mon Jun 06, 2011 9:25 pm

cool.thanks a lot!

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vinitrathi1: Newbie | Next Rank: 10 Posts; Posts: 8; Joined: Sun Jun 05, 2011 2:34 pm; Thanked: 2 times

by vinitrathi1 » Thu Jun 09, 2011 9:50 am

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?

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cans: Legendary Member; Posts: 1309; Joined: Mon Apr 04, 2011 5:34 amFollowed by: 123 members; Location: India; Thanked: 310 times; GMAT Score:750

by cans » Fri Jun 10, 2011 6:42 am

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

If my post helped you- let me know by pushing the thanks button

Contact me about long distance tutoring!
[email protected]

Cans!!

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