briana.img
  • briana.img
Find the number of ways to listen to 4 different CDs from a selection of 15 CDs.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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briana.img
  • briana.img
I thought it was 15*14*13*12 but it's not
jim_thompson5910
  • jim_thompson5910
That would be the answer if order mattered, but it does not matter
jim_thompson5910
  • jim_thompson5910
Let's say you had 4 CDs labeled A,B,C,D there are 4! = 4*3*2*1 = 24 ways to arrange the four letters (eg: ABCD or ACBD) you have to divide the answer you got by 24 to account for the fact that order doesn't matter

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briana.img
  • briana.img
aaaah okay okay so 1365
jim_thompson5910
  • jim_thompson5910
Smaller example Let's say you had 4 CDs (A,B,C,D) and you pick 2 of them. order doesn't matter 4*3 = 12 if order mattered. The full list of choices is AB, BA AC, CA AD, DA BC, CB BD, DB CD, DC notice how the list above is double of what it should be. We've counted everything twice. Which is why we divide by 2! = 2*1 = 2 to get 12/2 = 6. There are 6 ways to pick the two CDs where order doesn't matter
jim_thompson5910
  • jim_thompson5910
yes it is 1365 an alternative route is to use the combination formula \[\Large C(n,r) = \frac{n!}{r!*(n-r)!}\]
briana.img
  • briana.img
aaaaah okay okay!!

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