A sled needs to be pulled by a team of 4 huskies, chosen from a group of 10 available huskies. How many different 4-dog teams of huskies can be selected to pull the sled? 165 210 220 5,040
Question
A sled needs to be pulled by a team of 4 huskies, chosen from a group of 10 available huskies. How many different 4-dog teams of huskies can be selected to pull the sled? 165 210 220 5,040
Solution
The problem can be solved using the combination formula, which is used when the order of selection does not matter. The formula is:
C(n, k) = n! / [k!(n-k)!]
where:
- n is the total number of options,
- k is the number of options to choose,
- "!" denotes factorial, meaning the product of all positive integers up to that number.
In this case, n = 10 (the total number of huskies) and k = 4 (the number of huskies to select for the team).
So, the calculation would be:
C(10, 4) = 10! / [4!(10-4)!] = (10987654321) / [(4321)(654321)] = (10987) / (4321) = 210
So, there are 210 different 4-dog teams of huskies that can be selected to pull the sled.
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