This problem is covered in elementary statistics first year university. The number of combinations can be calculated with the following formula:

    X
N =  C
      Y
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Which stands for give me the number of combinations by picking Y items from a total of X number of items. The mathematical expansion of the above formula becomes:

    X      X(x) * X(x-1) * ... * X(y+1)
N =  C  =  ----------------------------
      Y       1 * 2 * ... (x - y)
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To pick 6 numbers from 7 numbers = 7C6 = 7/1 = 7 possible ways.

To pick 6 numbers from 8 numbers = 8C6 = 8*7/1*2 = 28.

To pick 6 numbers from 9 numbers = 9C6 = 9*8*7/1*2*3 = 84.

The perl for calculating the number of combinations is thus:

use strict;

sub xCy()
{
    my ($x, $y) = @_;
    return(0) if $x < $y;   # can not pick more number than given
    return(1) if $x == $y;  # 1 combination if X = Y

    my $diff = $x - $y;
    my $n = 1;
    for (0 .. $diff-1) { $n *= $x - $_ }
    my $m = 1;
    for (1 .. $diff) { $m *= $_ }

    return $n / $m;
}

printf "%d\n", &xCy($_, 6) for 7 .. 10;

__END__
7
28
84
210
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