anonymous
  • anonymous
find the numbers of permutations 10P6
Mathematics
jamiebookeater
  • jamiebookeater
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jim_thompson5910
  • jim_thompson5910
do you have any ideas on the first step?
anonymous
  • anonymous
\[_{10} P _{6}\]
anonymous
  • anonymous
no

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jim_thompson5910
  • jim_thompson5910
Are you familiar with the permutation formula?
anonymous
  • anonymous
no
jim_thompson5910
  • jim_thompson5910
If not, the permutation formula is n P r = (n!)/((n-r)!) where n! means n! = n*(n-1)*(n-2)*...*3*2*1 For example: 6! = 6*5*4*3*2*1
jim_thompson5910
  • jim_thompson5910
So in our case, 10 P 6 is 10 P 6 = (10!)/((10-6)!) since n = 10 and r = 6
jim_thompson5910
  • jim_thompson5910
Can you take it from here or do you need more help?
anonymous
  • anonymous
yes i need more help please
jim_thompson5910
  • jim_thompson5910
(10!)/((10-6)!) will become (10!)/(4!) since 10-6 = 4
jim_thompson5910
  • jim_thompson5910
Then you expand out 10! like so 10*9*8*7*6*5*4! We stop at 4 because the "4!" terms will cancel So (10!)/(4!) turns into (10*9*8*7*6*5*4!)/(4!) and the "4!" terms will cancel leaving us with 10*9*8*7*6*5
jim_thompson5910
  • jim_thompson5910
Last step is to multiply out 10*9*8*7*6*5 to get your answer

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