SOLUTION: Six students are to be chosen from a class of 18 to represent the class at a math contest. How many ways can the six students be chosen?

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Question 580374: Six students are to be chosen from a class of 18 to represent the class at a math contest. How many ways can the six students be chosen?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
There are 18 ways to choose the first person

There are 17 ways to choose the second person (since a single person can't be chosen twice)

There are 16 ways to choose the third person

There are 15 ways to choose the fourth person

There are 14 ways to choose the fifth person

There are 13 ways to choose the sixth person


Multiply these all together to get: 18*17*16*15*14*13 = 13366080


So there are 13366080 different ways assuming order matters.

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If order does NOT matter, then this means that you've been overcounting. To fix this issue, you need to divide by 6! = 6*5*4*3*2*1 = 720 to get

13366080/720 = 18564


So there are 18564 different ways assuming order does NOT matter.