There are 6 seniors on student council. Two of them will be chosen to go to an all-district meeting. How many ways are there to choose the students who will go to the meeting?Decide if this is a permutation or a combination, and then find the number of ways to choose the students who go.A.Combination; number of ways = 15B.Permutation; number of ways = 15C.Combination; number of ways = 30D.Permutation; number of ways = 30
Question
There are 6 seniors on student council. Two of them will be chosen to go to an all-district meeting. How many ways are there to choose the students who will go to the meeting?Decide if this is a permutation or a combination, and then find the number of ways to choose the students who go.A.Combination; number of ways = 15B.Permutation; number of ways = 15C.Combination; number of ways = 30D.Permutation; number of ways = 30
Solution
This is a combination problem, not a permutation. This is because the order in which the students are chosen does not matter.
In a combination, the order does not matter. If you have 6 students and you want to choose 2, it doesn't matter which one you choose first or second, you're still ending up with the same 2 students.
The formula for combinations is:
nCr = n! / r!(n - r)!
where:
- n is the total number of options,
- r is the number of options chosen at a time,
- "!" denotes a factorial, meaning the product of all positive integers up to that number.
So, in this case, we have 6 students and we are choosing 2.
So,
6C2 = 6! / 2!(6 - 2)!
= (654321) / (214321)
= 15
So, there are 15 ways to choose 2 students from 6.
Therefore, the answer is A. Combination; number of ways = 15.
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