I am trying to calculate the number of treble bets for any given number of selections. A treble is a bet where 3 different selections in 3 different events are combined. So, selection a in event 1 selection b in event 2 and selection c in event 3 constitute a treble.
I can calculate the number of trebles for a given number of selections
4 selections = 4 trebles, 5 = 10, 6 = 20, but what I can't calculate, and need help with is the effect of a non runner. If there is 1 non runner say selection a, then each bet containing selection a becomes a double ie abc becomes a doulbe bc. If there are 2 non runners then each bet containing those non runners becomes a single ie abc becomes single c. If all three selections are non runners then the bet becomes void. I hope the following table illustrates more accurately what I mean. For 5 selections
sel nr treble double single void 5 0 10 0 0 0 4 1 4 6 0 0 3 2 1 6 3 0 2 3 0 3 6 1 1 4 0 0 6 4 0 5 0 0 0 0
Clearly there is a pattern but I cannot figure out how the pattern is arrived at, or how to calculate the effect of X non runners on treble bets of N selections. Please can anyone help. Many thanks.