SOLUTION: evaluate this expression in details please: 4P3 / 8P3

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Question 94329: evaluate this expression in details please: 4P3 / 8P3
Answer by jim_thompson5910(21667) About Me  (Show Source):
You can put this solution on YOUR website!
Start with the given expression



First lets evaluate the numerator:



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



4%21%2F%284-3%29%21 Plug in n=4 and r=3



4%21%2F1%21 Subtract 4-3 to get 1



Expand 4!
%284%2A3%2A2%2A1%29%2F1%21



Expand 1!
%284%2A3%2A2%2A1%29%2F%281%29



%284%2A3%2A2%2Across%281%29%29%2F%28cross%281%29%29 Cancel



4%2A3%2A2 Simplify




24 Now multiply 4*3*2 to get 24





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Now lets evaluate the denominator:




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



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



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



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



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



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



8%2A7%2A6 Simplify




336 Now multiply 8*7*6 to get 336


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So


Now reduce 24%2F336 to get 1%2F14




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Answer:


So