n * [(n – 1)/2]
For n things, taken three and three together, the number is
n * [(n – 1)/2] * [(n – 2)/3]
For n things, taken four and four together, the number is
n * [(n – 1)/2] * [(n – 2)/3] * [(n – 3)/4]
Applying these formulæ to policy, it will be seen that to ascertain the number of "saddles" in any combination you multiply by the next number under and divide by 2; for "gigs," multiply by the next two numbers under and divide by 6; while for "horses" you multiply the next three numbers under and divide by 24. Thus,
78 X [(78 – 1)/2] = 3,003 "saddles."
78 X [(78 – 1)/2] X [(78 – 2)/3] = 76,076 "gigs."
78 X [(78 – 1)/2] X [(78 – 2)/3] X [(78 – 3)/4] = 1,426,425 "horses."
In other words, there are 3,003 "saddles" in 78 numbers, and it follows that any person playing a capital has two chances in his favor and 3,001 against him.