SOLUTION: Evaluate: 8C3 11 56 24 336

Algebra ->  Permutations -> SOLUTION: Evaluate: 8C3 11 56 24 336       Log On


   

Question 470766: Evaluate: 8C3
11
56
24
336
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

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


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



8%21%2F%288-3%29%213%21 Plug in n=8 and r=3



8%21%2F5%213%21 Subtract 8-3 to get 5


Expand 8!
%288%2A7%2A6%2A5%2A4%2A3%2A2%2A1%29%2F5%213%21


Expand 5!
%288%2A7%2A6%2A5%2A4%2A3%2A2%2A1%29%2F%285%2A4%2A3%2A2%2A1%293%21



%288%2A7%2A6%2Across%285%2A4%2A3%2A2%2A1%29%29%2F%28cross%285%2A4%2A3%2A2%2A1%29%293%21 Cancel



%288%2A7%2A6%29%2F3%21 Simplify


Expand 3!
%288%2A7%2A6%29%2F%283%2A2%2A1%29



336%2F%283%2A2%2A1%29 Multiply 8*7*6 to get 336



336%2F6 Multiply 3*2*1 to get 6



56 Now divide



So 8 choose 3 (where order doesn't matter) yields 56 unique combinations