peteprobs = [0] * 37 colinprobs = [0] * 37 from useful import choose, multinom for num1s in range(10) : for num2s in range(10-num1s) : for num3s in range(10-num1s-num2s) : num4s = 9 - num1s - num2s - num3s peteprobs[num1s + 2*num2s + 3*num3s + 4*num4s] += multinom(9,num1s,num2s,num3s,num4s) * 0.25**9 for num1s in range(7) : for num2s in range(7-num1s) : for num3s in range(7-num1s-num2s) : for num4s in range(7-num1s-num2s-num3s) : for num5s in range(7-num1s-num2s-num3s-num4s) : num6s = 6-num1s-num2s-num3s-num4s-num5s colinprobs[num1s + 2*num2s + 3*num3s + 4*num4s + 5*num5s + 6*num6s] += multinom(6,num1s,num2s,num3s,num4s,num5s,num6s) * (float(1)/6)**6 tot = 0 for p in range(len(peteprobs)) : for c in range(len(colinprobs)) : if p > c : tot += peteprobs[p] * colinprobs[c] print tot
# Find the number of ways that twenty 12-sided die can be rolled so the top ten dice sum to 70 from useful import allSums, choose, multinom, fact topNum = 10 totalNum = 20 diceLeft = totalNum-topNum diceVal = 12 sumTo = 70 allWays = 0 for sum in allSums(topNum,sumTo,1,diceVal) : counts = [0] * diceVal for dig in sum : counts[dig-1] += 1 upperBound = sum[0] thisManyWays = 0 for reps in xrange(diceLeft+1) : counts[upperBound-1] += reps thisManyWays += multinom(totalNum, *(counts)) * (upperBound-1)**(diceLeft-reps) / fact(diceLeft-reps) counts[upperBound-1] -= reps allWays += thisManyWays print allWays
