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10 Arabian horses are split into pairs to pull one of the

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Manager
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Joined: 25 Nov 2009
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10 Arabian horses are split into pairs to pull one of the [#permalink]

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New post 06 Jun 2010, 08:57
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Question Stats:

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10 Arabian horses are split into pairs to pull one of the distinct 4 carts in a race. If each cart is assigned to a pair, how many different assignments of horses to carts are possible?

A, 420
B. 1260
C. 5220
D. 9450
E. 113400

Note: Found this question. But not the OA. Can anyone help? Thanks in advance.
[Reveal] Spoiler: OA

Last edited by Bunuel on 30 Jun 2013, 13:40, edited 1 time in total.
Added the OA
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Re: Pairs of Horses and Carts [#permalink]

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New post 06 Jun 2010, 09:37
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Expert's post
jusjmkol740 wrote:
10 Arabian horses are split into pairs to pull one of the distinct 4 carts in a race. If each cart is assigned to a pair, how many different assignments of horses to carts are possible?

a) 420
b) 1260
c) 5220
d) 9450
e) 113400

Note: Found this question. But not the OA. Can anyone help? Thanks in advance.


Note: The question is beyond the GMAT scope.

# of ways 10 horses can be divided into 5 groups when order of the groups does not matter is: \(\frac{C^2_{10}*C^2_{8}*C^2_{6}*C^2_{4}*C^2_{2}}{5!}=945\).

So we would have 945 different cases of dividing 10 horses into 5 groups:
1. \(A_1\), \(B_1\), \(C_1\), \(D_1\), \(E_1\) (each letter represent pair of horses);
2. \(A_2\), \(B_2\), \(C_2\), \(D_2\), \(E_2\);
...
945. \(A_{945}\), \(B_{945}\), \(C_{945}\), \(D_{945}\), \(E_{945}\).

Now, we want to assign a pair (a letter in our case) to one of 4 distinct carts. For each case (out of 945) \(P^4_5=120\) would represent # of ways to choose 4 pairs out of 5 when order matters (as carts are distinct). OR \(C^4_5\) - choose 4 different letters out of 5 and \(4!\) - # of ways to assign 4 different letters to 4 distinct carts: \(C^4_5*4!=120\).

So total # of different assignments would be \(945*120=113400\).

Answer: E.

Questions about the same concept:

probability-85993.html?highlight=divide+groups
combination-55369.html#p690842
probability-88685.html#p669025
combination-groups-and-that-stuff-85707.html#p642634
sub-committee-86346.html?highlight=divide+groups
combinations-problems-95344.html#p733805

Hope it helps.
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Manager
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Joined: 25 Nov 2009
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Location: India
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Kudos [?]: 38 [0], given: 8

Re: Pairs of Horses and Carts [#permalink]

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New post 07 Jun 2010, 12:42
Thanks Bunnel.
But I'm still a bit confused about the explanation. Some more elaboration would certainly help.
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Re: Pairs of Horses and Carts [#permalink]

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New post 07 Jun 2010, 12:49
Expert's post
jusjmkol740 wrote:
Thanks Bunnel.
But I'm still a bit confused about the explanation. Some more elaboration would certainly help.


Please go through the links in my previous post to understand the concept, also see the newest topic with similar problem at: combinations-problems-95344.html.

Hope it helps.
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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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Ten Arabian horses are split into pairs to pull one of the distinct [#permalink]

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New post 12 Sep 2014, 11:33
Ten Arabian horses are split into pairs to pull one of the distinct 4 carts in a race.
If each cart is assigned to a pair of horses, how many different assignments of
horses to cart are possible?

a 420
b 1260
c 5220
d 9450
e 113400
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 34121
Followers: 6109

Kudos [?]: 76952 [0], given: 9994

Re: 10 Arabian horses are split into pairs to pull one of the [#permalink]

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New post 12 Sep 2014, 11:49
Expert's post
manish2014 wrote:
Ten Arabian horses are split into pairs to pull one of the distinct 4 carts in a race.
If each cart is assigned to a pair of horses, how many different assignments of
horses to cart are possible?

a 420
b 1260
c 5220
d 9450
e 113400


Merging topics. Please do NOT post questions from questionable sources.
_________________

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?
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Re: 10 Arabian horses are split into pairs to pull one of the   [#permalink] 12 Sep 2014, 11:49
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