Combinatorics...

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jjenrico: Newbie | Next Rank: 10 Posts; Posts: 9; Joined: Wed Jan 21, 2009 12:45 am

Combinatorics...

by jjenrico » Thu Feb 19, 2009 7:02 am

hi guys,

can you help me with this?

How many different signals can be transmitted by hoisting 3 red, 4 yellow and 2 blue flags on a pole, assuming that in transmitting a signal all nine flags are to be used?

I don't have the options, but how do I approach it??

thanks!

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Source: Beat The GMAT — Problem Solving | Thu Feb 19, 2009 7:02 am

x2suresh: Master | Next Rank: 500 Posts; Posts: 258; Joined: Thu Aug 07, 2008 5:32 am; Thanked: 16 times

Re: Combinatorics...

by x2suresh » Thu Feb 19, 2009 7:17 am

jjenrico wrote:hi guys,

can you help me with this?

How many different signals can be transmitted by hoisting 3 red, 4 yellow and 2 blue flags on a pole, assuming that in transmitting a signal all nine flags are to be used?

I don't have the options, but how do I approach it??

thanks!

9!/(3! *4! * 2!)

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jjenrico: Newbie | Next Rank: 10 Posts; Posts: 9; Joined: Wed Jan 21, 2009 12:45 am

by jjenrico » Thu Feb 19, 2009 7:38 am

x2suresh

can you pls explain why?

thanks!

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Mr2Bits: Senior | Next Rank: 100 Posts; Posts: 73; Joined: Wed Jan 07, 2009 1:00 pm; Location: Tampa, FL; Thanked: 9 times; GMAT Score:630

by Mr2Bits » Thu Feb 19, 2009 7:49 am

total combinations possible (9!) / possibilities you have (4! of the yellow flags * 3! combinations of Red * 2! combinations of the blue)

Answer should be 15120

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mals24: Legendary Member; Posts: 683; Joined: Tue Jul 22, 2008 1:58 pm; Location: Dubai; Thanked: 73 times; Followed by:2 members

by mals24 » Thu Feb 19, 2009 7:56 am

The question is asking in how many ways can you arrange the letters RRRYYYYBB

The number of ways of arranging 9 flags = 9!

Now we divide 3!*4!*2! to account for the letters that are repeated.

So the answer should be 9!/3!*4!*2!

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Stuart@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pm; Location: Toronto; Thanked: 1710 times; Followed by:614 members; GMAT Score:800

by Stuart@KaplanGMAT » Thu Feb 19, 2009 1:14 pm

There are two different permutations formulas that it's good to know for Test Day.

1) If we have n unique items and we want to arrange k of them, then the total number of arrangements is:

n!/(n-k)!

2) If we have n items to arrange, but some of them are identical, then the total number of arrangements is:

n!/r!s!t!...

in which r, s and t are the number of duplicate items.

This is most commonly tested on the GMAT in word jumble questions. Here are some examples:

In how many different ways can the letters of the word "DESERT" be arranged?

6 total letters, 2 duplicate "E"s, so 6!/2!

In how many different ways can the letters of the word "DESSERT" be arranged?

7 total letters, 2 duplicate "E"s and 2 duplicate "S"s so 7!/2!2!

In how many different ways can the letters of the word "DESSERTS" be arranged?

8 total letters, 2 duplicate "E"s and 3 duplicate "S"s, so 8!/2!3!

In the question posted in this thread, we have 9 total items with 3 duplicate reds, 4 duplicate yellows and 2 duplicate blues, so our answer is:

9!/3!4!2!