Combinatorics

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  • #70881
    Shreya Nair
    Participant

    Is the solution correct?

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    #74639
    Shirsendu Roy
    Moderator

    There are 4 even numbers and 4 odd numbers

    if an even and odd number is paired then no pair of gcd 2

    which is 4!=24 ways.

    the order of odd numbers can be shuffled that many different ways in each case pairing the first odd number with 2, the second one with 4, and so on.

    if even and odd are not paired then

    two even numbers is paired

    here the pair of even numbers in the set that have gcd not 2 is 4 and 8.

    so pair of 4 and 8 taken.

    choose two odd numbers to pair together in {4 \choose 2}=6 different ways and pair the remaining two odd numbers in 2 different ways with 2 and 6

    which gives (2)(6)=12 different ways

    so two methods give 24+12=36 ways.

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