Ricorriamo allo script calcolatrice.
Calcolo   C(100,2) = 4950, ..., C(100,10) = 17310309456440
E poi:
pow(1/8,0)*pow(7/8,100) + pow(1/8,1)*pow(7/8,99)*100 + pow(1/8,2)*pow(7/8,98)*4950 + pow(1/8,3)*pow(7/8,97)*161700 + pow(1/8,4)*pow(7/8,96)*3921225 + pow(1/8,5)*pow(7/8,95)*75287520 + pow(1/8,6)*pow(7/8,94)*1192052400 + pow(1/8,7)*pow(7/8,93)*16007560800 + pow(1/8,8)*pow(7/8,92)*186087894300 + pow(1/8,9)*pow(7/8,91)*1902231808400 + pow(1/8,10)*pow(7/8,90)*17310309456440
ottenendo:
0.28099917939852637