In the combination formula nCk n=20 k=5 first subset is 1,2,3,4,5 last subset is 16,17,18,19,20?

What is the position in the sequence of subset 3,11,13,17,19 ?

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  • 1 decade ago
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    There are 19C4 combinations of the form

    1,x,x,x,x

    and

    18C4 of the form

    2,x,x,x,x

    3,4,x,x,x = 16C3

    3,5,x,x,x = 15C3

    and so on up to

    3,10,x,x,x = 10C3

    3,11,12,x,x = 8C2

    3,11,13,14,x = 6C1

    3,11,13,15,x = 5C1

    3,11,13,16,x = 4C1

    3,11,13,17,18 = 1C1

    and the one after that is

    3,11,13,17,19

    So you have

    19C4 + 18C4 + 16C3 + 15C3 + 14C3 + 13C3 + 12C3 + 11C3 + 10C3 + 8C2 + 6C1 + 5C1 + 4C1 + 1C1 = 9150

    and then you have

    #9151

    Source(s): Verified by actually doing it (by computer).
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