Building out a web dev portfolio. For a web app I am working with lottery probabilities.
How many combinations are there if I only choose combinations within observed maximum and minimum values? Here are the stats:
The lottery I'm starting with is Mega Millions. 5 numbers drawn and not replaced from 1-75, with a sixth number chosen from 1-15.
C(75,5) * 15 = 258,890,850 combinations
My attempt is:
All combinations within maximums observed. ( 43 * (64-1) * (68-2) * (74-3) * (75-4) ) / 5! * 15 = 112,662,569.25 Less combinations below minimums observed. ( (3-1) * (8-2) * (20-3) * (23-4) ) / 4! = 161.5 Combinations within maximum & minimum limits = 112,662,407
Is there a better approach to calculating the number of combinations within constraints?