SOLUTION: EVALUATE EACH EXPRESSION: 7P3

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Question 94281: EVALUATE EACH EXPRESSION: 7P3
Answer by jim_thompson5910(14896) About Me  (Show Source):
You can put this solution on YOUR website!

Since order does matter, we can use the permutation formula:




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



7%21%2F%287-3%29%21 Plug in n=7 and r=3



7%21%2F4%21 Subtract 7-3 to get 4



Expand 7!
%287%2A6%2A5%2A4%2A3%2A2%2A1%29%2F4%21



Expand 4!
%287%2A6%2A5%2A4%2A3%2A2%2A1%29%2F%284%2A3%2A2%2A1%29



%287%2A6%2A5%2Across%284%2A3%2A2%2A1%29%29%2F%28cross%284%2A3%2A2%2A1%29%29 Cancel



7%2A6%2A5 Simplify




210 Now multiply 7*6*5 to get 210


So 7 choose 3 (where order does matter) yields 210 unique combinations