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01 May 2019, 00:10
Kudos
Bookmarks
E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
56% (02:18) correct
44%
(02:11)
wrong
based on 329
sessions
History
Date
Time
Result
Not Attempted Yet
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
A. 32
B. 64
C. 420
D. 1680
E. 2520
01 May 2019, 01:25
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Bookmarks
Bunuel
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
20 Jan 2021, 15:56
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Bunuel
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
