grade 8 math

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how many different ways can eight cars finish in a race 1st, 2nd, 3rd ?

  • grade 8 math -

    72

  • grade 8 math -

    336

  • grade 8 math -

    Ok if you have cars A B C D E F G H. Your options for the first three places are :
    ABC, ABD, ABE, ABF, ABG, ABH
    ACB, ACD, ACE, ACF, ACG, ACH
    ADB, ADC, ADE, ADF, ADG, ADH
    AEB, AEC, AED, AEF, AEG, AEH
    AFB, AFC, AFD, AFE, AFG, AFH
    AGB, AGC, AGD, AGE, AGF, AGH
    AHB, AHC, AHD, AHE, AHF, AHG

    6 x 7 = 42 options with car A in first place.

    you can go through and do the same thing with each car in first place...
    BAC, BAD, BAE..... HGD, HGE, HGF...

    But to do it mathematically ~ 8 cars, 42 options with each car in first place.
    42 x 8 = 336 different ways eight cars can finish a race in first, second and third place.

  • grade 8 math -

    1,000,000,000

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