The factorial one was buried in the subconcious, stemmed from talking with race gamblers and soccer pools punters yonks ago..
Combinations !! BTW pools 'perms' incorrectly named !!
How do you calculate any 4 selections taken together from 7 selections ?
( 7x6x5x4 ) / ( 4x3x2x1 ) this becomes generalised 7! / (4! x ( 7 - 4 )!)
= 35 bets
Hence soccer pools any 8 from 12 = 12 ! / ( 8! x ( 12 - 8 ) ! )
=> 479,001,600 / ( 40,320 x 24 ) => 479,001,600 / 967,680
The result being 495 combinations of any 8 from 12.
ie pools 'treble chance' mark 12 x's in a column if any 8 are score draws then guaranteed to have min one line scoring 8 x 3 = 24 pts hence jackpot or share of, plus minor dividends
Suddenly realised p'raps no one knows about pools etc -- today.
Mis-spent yoof !!