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In how many different ways can trhee letters be posted from

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In how many different ways can trhee letters be posted from [#permalink] New post 10 Nov 2007, 12:00
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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 :)
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Re: counting principles [#permalink] New post 18 Nov 2009, 04:55
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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
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Re: counting principles [#permalink] New post 17 Feb 2010, 02:47
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
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Re: counting principles [#permalink] New post 10 Feb 2012, 03:03
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.
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Re: In how many different ways can trhee letters be posted from [#permalink] New post 10 Feb 2012, 04:05
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
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Re: counting principles [#permalink] New post 10 Feb 2012, 08:13
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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.
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NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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.


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Re: counting principles [#permalink] New post 25 May 2013, 07:22
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
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Re: counting principles [#permalink] New post 25 May 2013, 12:06
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
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Re: counting principles   [#permalink] 25 May 2013, 12:06
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