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Eight Alaskan Huskies are split into pairs to pull one of four sleds

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Bunuel
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Eight Alaskan Huskies are split into pairs to pull one of four sleds [#permalink] New post   01 May 2019, 00:10
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Eight Alaskan Huskies are split into pairs to pull one of four sleds in a race. How many different assignments of Huskies to sleds are possible?

A. 32
B. 64
C. 420
D. 1680
E. 2520
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Eight Alaskan Huskies are split into pairs to pull one of four sleds [#permalink] New post   01 May 2019, 01:25
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Bunuel wrote:
Eight Alaskan Huskies are split into pairs to pull one of four sleds in a race. How many different assignments of Huskies to sleds are possible?

A. 32
B. 64
C. 420
D. 1680
E. 2520


We have to make 4 pairs out of 8 and assign them at 4 sleds

first pair can be made in 8C2 = 28 ways
Second pair can be made in 6C2 = 15 ways
Third pair can be made in 4C2 = 6 ways
Forth pair can be made in 2C2 = 1 ways

i.e. Required Outcome \(= 8C2*6C2*4C2*2C2= 28*15*6*1 = 2520\)

Answer: Option E
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Re: Eight Alaskan Huskies are split into pairs to pull one of four sleds [#permalink] New post   01 May 2019, 02:35
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Bunuel wrote:
Eight Alaskan Huskies are split into pairs to pull one of four sleds in a race. How many different assignments of Huskies to sleds are possible?

A. 32
B. 64
C. 420
D. 1680
E. 2520


total pairs possible
8c2*6c2*4c2*2c2 ; 2520
IMO E
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Re: Eight Alaskan Huskies are split into pairs to pull one of four sleds [#permalink] New post   17 Nov 2019, 08:08
Archit3110 wrote:
Bunuel wrote:
Eight Alaskan Huskies are split into pairs to pull one of four sleds in a race. How many different assignments of Huskies to sleds are possible?

A. 32
B. 64
C. 420
D. 1680
E. 2520


total pairs possible
8c2*6c2*4c2*2c2 ; 2520
IMO E


Archit3110
It doesn't matter how we assign those pairs to 4 sleds? So let's say the pair formed from 8C2 can be assigned in 4 ways?

Or that will be a different approach to this question.
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Re: Eight Alaskan Huskies are split into pairs to pull one of four sleds [#permalink] New post   20 Jan 2021, 15:56
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Bunuel wrote:
Eight Alaskan Huskies are split into pairs to pull one of four sleds in a race. How many different assignments of Huskies to sleds are possible?

A. 32
B. 64
C. 420
D. 1680
E. 2520

Solution:

First, there are [8C2 x 6C2 x 4C2 x 2C2] / 4! = [(8 x 7)/2 x (6 x 5) / 2 x (4 x 3) / 2] / 24 = [28 x 15 x 6] / 24 = 105 ways to split 8 Huskies into 4 pairs. (Notice that 8C2 is the number of ways the first pair could be chosen, 6C2 the second, 4C2 the third, and 2C2 the fourth. But once 4 pairs are chosen, it doesn’t matter how we arrange them, they are still the same 4 pairs; therefore, we need to divide by 4!).

Second, for every set of 4 pairs, there are 4! = 24 ways the 4 sleds can be assigned to them. Therefore, there are a total of 105 x 24 = 2520 different assignments.

Answer: E
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Re: Eight Alaskan Huskies are split into pairs to pull one of four sleds [#permalink] New post   17 Dec 2023, 19:44
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Re: Eight Alaskan Huskies are split into pairs to pull one of four sleds [#permalink]
17 Dec 2023, 19:44
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