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The Peanuts (Posted on 2003-02-18) Difficulty: 3 of 5
Although some of the things in this problem aren't true in real life just assume they are in the question.

When growing peanuts the following happens:

  • for every 2 single chambered peanuts there will be one double chambered peanut
  • for every 2 double chambered peanuts there will be one triple chambered peanut
  • for every 2 triple chambered peanuts there will be one quadruple chambered peanut.

    When a company packages 1000 peanuts in one bag they take peanuts randomly from a giant bin that contins all the peanuts grown. What are the odds that there will be 1000 individual nuts?

  • See The Solution Submitted by Alan    
    Rating: 3.7500 (4 votes)

    Comments: ( Back to comment list | You must be logged in to post comments.)
    re: Slight Correction | Comment 9 of 11 |
    (In reply to Slight Correction by Charlie)

    As a check, here's the program logic; it goes through all sum of compartments = 1000 and counts only those adding to 577:
    80 P1=15:P2=15/2:P3=15/4:P4=15/8
    90 point 25
    100 T=1000
    110 for Quad=0 to int(1000/4)
    120 T2=T-Quad*4
    130 for Trip=0 to int(T2/3)
    140 T3=T2-Trip*3
    150 for Dbl=0 to int(T3/2)
    160 Sngl=T3-Dbl*2
    161 if Quad+Trip+Dbl+Sngl=577 then
    162 :W=combi(577,Quad)*combi(577-Quad,Trip)*combi(577-Quad-T
    rip,Dbl)
    163 :P=P1^Quad*P2^Trip*P3^Dbl*P4^Sngl
    164 :Tp=Tp+W/P
    170 next
    180 next
    190 next
    200 print Tp
      Posted by Charlie on 2003-02-24 09:13:00

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