Author 
Message 
TAGS:

Hide Tags

VP
Joined: 09 Jul 2007
Posts: 1100
Location: London

In how many different ways can trhee letters be posted from [#permalink]
Show Tags
10 Nov 2007, 13:00
3
This post was BOOKMARKED
Question Stats:
47% (02:37) correct
53% (02:15) wrong based on 24 sessions
HideShow timer Statistics
1. In how many different ways can trhee letters be posted from seven different postboxes assuming no two letters can be posted from the same postbox?
2. what if there is no restriction, that is, if two or more letters can be posted from the same box?
warm up



Math Expert
Joined: 02 Sep 2009
Posts: 39589

Re: counting principles [#permalink]
Show Tags
18 Nov 2009, 05:55
4
This post received KUDOS
Expert's post
2
This post was BOOKMARKED



Senior Manager
Joined: 22 Dec 2009
Posts: 359

Re: counting principles [#permalink]
Show Tags
17 Feb 2010, 03:47
Ravshonbek wrote: 1. In how many different ways can trhee letters be posted from seven different postboxes assuming no two letters can be posted from the same postbox? 2. what if there is no restriction, that is, if two or more letters can be posted from the same box? warm up 1. 7 x 6 x 5 = 210 2. 7 x 7 x 7 = 343
_________________
Cheers! JT........... If u like my post..... payback in Kudos!!
Do not post questions with OAPlease underline your SC questions while postingTry posting the explanation along with your answer choice For CR refer Powerscore CR BibleFor SC refer Manhattan SC Guide
~~Better Burn Out... Than Fade Away~~



Verbal Forum Moderator
Joined: 23 Oct 2011
Posts: 283

Re: counting principles [#permalink]
Show Tags
10 Feb 2012, 04:03
Bunuel wrote: 1. In how many different ways can trhee letters be posted from seven different postboxes assuming no two letters can be posted from the same postbox?
First letter could be sent from ANY of the seven postboxes  7 (7 options); Second letter could be sent from the SIX postboxes left  6 (6 options); Third letter could be sent from the FIVE postboxes left  5 (5 options);
Total # of ways =7*6*5=210
2. what if there is no restriction, that is, if two or more letters can be posted from the same box?
In this problem we don't have restriction, thus ANY letter could be sent from ANY postboxes =7*7*7=7^3=343 Hi Bunuel, Could you please elaborate on the second question. Couldn't figure out why.
_________________
******************** Push +1 kudos button please, if you like my post.



Manager
Joined: 10 Jan 2010
Posts: 185
Location: Germany
Concentration: Strategy, General Management
GPA: 3
WE: Consulting (Telecommunications)

Re: In how many different ways can trhee letters be posted from [#permalink]
Show Tags
10 Feb 2012, 05:05
1. 7 (no restriction) * 6 (can not be the same as the first one) * 5 (can not be the same as the first and second one) = 210 2. 7 (no restriction) * 7 (no restriction) * 7 (no restriction) = 343



Math Expert
Joined: 02 Sep 2009
Posts: 39589

Re: counting principles [#permalink]
Show Tags
10 Feb 2012, 09:13
mohankumarbd wrote: Bunuel wrote: 1. In how many different ways can trhee letters be posted from seven different postboxes assuming no two letters can be posted from the same postbox?
First letter could be sent from ANY of the seven postboxes  7 (7 options); Second letter could be sent from the SIX postboxes left  6 (6 options); Third letter could be sent from the FIVE postboxes left  5 (5 options);
Total # of ways =7*6*5=210
2. what if there is no restriction, that is, if two or more letters can be posted from the same box?
In this problem we don't have restriction, thus ANY letter could be sent from ANY postboxes =7*7*7=7^3=343 Hi Bunuel, Could you please elaborate on the second question. Couldn't figure out why. Welcome to GMAT Club. Please find below answer to your question: "Two or more letters can be posted from the same box" means that all 3 letters can be posted from the same postbox (so we don't have the restriction we had for the first question). Now, since there are 7 postboxes then each of these 3 letters has 7 options to be posted from, total # of ways is 7*7*7=7^3. Hope it's clear.
_________________
New to the Math Forum? Please read this: All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Manager
Joined: 14 Nov 2011
Posts: 149
Location: United States
Concentration: General Management, Entrepreneurship
GPA: 3.61
WE: Consulting (Manufacturing)

Re: counting principles [#permalink]
Show Tags
25 May 2013, 08:22
Bunuel wrote: mohankumarbd wrote: Bunuel wrote: 1. In how many different ways can trhee letters be posted from seven different postboxes assuming no two letters can be posted from the same postbox?
First letter could be sent from ANY of the seven postboxes  7 (7 options); Second letter could be sent from the SIX postboxes left  6 (6 options); Third letter could be sent from the FIVE postboxes left  5 (5 options);
Total # of ways =7*6*5=210
2. what if there is no restriction, that is, if two or more letters can be posted from the same box?
In this problem we don't have restriction, thus ANY letter could be sent from ANY postboxes =7*7*7=7^3=343 Hi Bunuel, Could you please elaborate on the second question. Couldn't figure out why. Welcome to GMAT Club. Please find below answer to your question: "Two or more letters can be posted from the same box" means that all 3 letters can be posted from the same postbox (so we don't have the restriction we had for the first question). Now, since there are 7 postboxes then each of these 3 letters has 7 options to be posted from, total # of ways is 7*7*7=7^3. Hope it's clear. Hi Bunnel, I tried to do the second question via combinatorics, but i am not able to figure it out, please check the below method and guide where i went wrong = all three in one box +2 in one box and the last one in a different box + all three in different boxes = 3c3*7+3c2*7c1*6c5+3c1*7c3 = 7+ 3*7*6+3*7*6*5 = 7 + 126 + 270 = wrong



Manager
Joined: 27 Feb 2012
Posts: 136

Re: counting principles [#permalink]
Show Tags
25 May 2013, 13:06
Quote: I tried to do the second question via combinatorics, but i am not able to figure it out, please check the below method and guide where i went wrong
= all three in one box +2 in one box and the last one in a different box + all three in different boxes = 3c3*7+3c2*7c1*6c5+3c1*7c3 = 7+ 3*7*6+3*7*6*5 = 7 + 126 + 270 = wrong
Think it in this way, First letter can go to any 7 post offices Same case with second and same case with the third letter as well so 7*7*7
_________________

Please +1 KUDO if my post helps. Thank you.



GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15918

Re: In how many different ways can trhee letters be posted from [#permalink]
Show Tags
14 Jul 2014, 07:50
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up  doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources



Current Student
Joined: 21 Feb 2015
Posts: 10

Re: In how many different ways can trhee letters be posted from [#permalink]
Show Tags
21 Feb 2015, 21:53
Could someone please tell me why part 1 cannot be answered using "7C3" = 35 ways?
Many thanks.



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 9252
Location: United States (CA)
GRE 1: 340 Q170 V170

Re: In how many different ways can trhee letters be posted from [#permalink]
Show Tags
22 Feb 2015, 00:00
Hi icetray, Since the question is worded in a "vague" way, you bring up an interesting interpretation of it. Thankfully, questions on the Official GMAT are worded to remove ambiguity and "bias" on the part of the reader, so you won't have to worry about that on Test Day. This prompt reads as if it were created by the original poster, so it's not clear what he/she was "intending" the question to mean. As it is, your interpretation of the prompt makes a lot of sense  there does not seem to be any reason why we should emphasize the "order" of the letters (there's no reference to "first letter", "second letter", "third letter" and no reference to "arrangements"). Using postboxes ABC would be same as BCA, CBA, etc., so if we interpret the prompt as a "combinations" question, then 7c3 = 35 would be correct. GMAT assassins aren't born, they're made, Rich
_________________
760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com
Rich Cohen
CoFounder & GMAT Assassin
***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************



Intern
Joined: 01 Jan 2016
Posts: 11

Re: In how many different ways can trhee letters be posted from [#permalink]
Show Tags
06 Apr 2016, 08:41
Ravshonbek wrote: 1. In how many different ways can trhee letters be posted from seven different postboxes assuming no two letters can be posted from the same postbox? 2. what if there is no restriction, that is, if two or more letters can be posted from the same box? warm up 3. What if we assume no three letters can be posted from same postbox?




Re: In how many different ways can trhee letters be posted from
[#permalink]
06 Apr 2016, 08:41







