SOLUTION: How many different groups of 5 objects can be chosen from 9 objects? Please show your work, thank you very much.

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Question 195136: How many different groups of 5 objects can be chosen from 9 objects? Please show your work, thank you very much.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'm assuming that order doesn't matter.


Since order does not matter, we must use the combination formula:


n%21%2F%28n-r%29%21r%21 Start with the given formula



9%21%2F%289-5%29%215%21 Plug in n=9 and r=5



9%21%2F4%215%21 Subtract 9-5 to get 4


Expand 9!
%289%2A8%2A7%2A6%2A5%2A4%2A3%2A2%2A1%29%2F4%215%21


Expand 4!
%289%2A8%2A7%2A6%2A5%2A4%2A3%2A2%2A1%29%2F%284%2A3%2A2%2A1%295%21



%289%2A8%2A7%2A6%2A5%2Across%284%2A3%2A2%2A1%29%29%2F%28cross%284%2A3%2A2%2A1%29%295%21 Cancel



%289%2A8%2A7%2A6%2A5%29%2F5%21 Simplify


Expand 5!
%289%2A8%2A7%2A6%2A5%29%2F%285%2A4%2A3%2A2%2A1%29



15120%2F%285%2A4%2A3%2A2%2A1%29 Multiply 9*8*7*6*5 to get 15,120



15120%2F120 Multiply 5*4*3*2*1 to get 120



126 Now divide



So 9 choose 5 (where order doesn't matter) yields 126 unique combinations