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8 October, 00:17

How many ways can 10 runners finish first, second, and third in a race?

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  1. 8 October, 00:24
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    Let's call the 10 runners A B C D E F G H I J

    ABC

    ABD

    ABE

    ABF

    ABG

    ABH

    ABI

    ABJ

    ACB

    ACD

    ACE

    ACF

    ACG

    ACH

    ACI

    ACJ

    ADB

    ADC

    ADE

    ADF

    ADG

    ADH

    ADI

    ADJ

    AEB

    AEC

    AED

    AEF

    AEG

    AEH

    AEI

    AEJ

    AFB

    AFC

    AFD

    AFE

    AFG

    AFH

    AFI

    AFJ

    AGB

    AGC

    AGD

    AGE

    AGF

    AGH

    AGI

    AGJ

    AHB

    AHC

    AHD

    AHE

    AHF

    AHG

    AHI

    AHJ

    AIB

    AIC

    AID

    AIE

    AIF

    AIG

    AIH

    AIJ

    AJB

    AJC

    AJD

    AJE

    AJF

    AJG

    AJH

    AJI

    The above is 60 different ways, but now B C D E F G H I J have to come first, and the proses starts again, until we have covered them all. I'm not going to write them all out but in theory, there is 540 different ways. 9*60=540.
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