SOLUTION: there are 12 trumpet players in the marching band, but there is only room for 3 of them in the jazz band. how many diffrent combinations of trumpet players could be selected for th

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Question 89823: there are 12 trumpet players in the marching band, but there is only room for 3 of them in the jazz band. how many diffrent combinations of trumpet players could be selected for the jazz band out of the 12?
a. 1728
b. 36
c. 1320
d. 220
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

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


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



12%21%2F%2812-3%29%213%21 Plug in n=12 and r=3



12%21%2F9%213%21 Subtract 12-3 to get 9


Expand 12!
%2812%2A11%2A10%2A9%2A8%2A7%2A6%2A5%2A4%2A3%2A2%2A1%29%2F9%213%21


Expand 9!




Cancel



%2812%2A11%2A10%29%2F3%21 Simplify


Expand 3!
%2812%2A11%2A10%29%2F%283%2A2%2A1%29



1320%2F%283%2A2%2A1%29 Multiply 12*11*10 to get 1,320



1320%2F6 Multiply 3*2*1 to get 6



220 Now divide



So 12 choose 3 (where order doesn't matter) yields 220 unique combinations

So the answer is d)