hw2 110590049

tags probability

problem 1

$\frac{4}{12} \times \frac{3}{8} \times \frac{2}{8} \times \frac{2}{4} = 1.56%$

$1 - \frac{c _{4}^{5} \times 4 !}{5 ^{4}} = 1 - 0.192 = 80.8%$

$1 - \frac{c _{4}^{48}}{c _{4}^{52}} = 1 - 0.718 = 28.1%$

$\frac{c _{8}^{11} \times 8 !}{1 1 ^{8}} = 3.1%$

Evey level at least have one people leave so only 3 people can chose leave level freely

$\frac{c _{3}^{6} * 3 ^{(6 - 3)}}{3 ^{6}} = \frac{20}{3 ^{3}} = 74%$

$3^{12} = 531441$

$\frac{12 !}{6 ! \times 6 !} = 924$

$\frac{12 !}{3 ! \times 4 ! \times 5 !} = 27720$

$1 - \frac{6 !}{6 ^{6}} = 1 - 0.015 = 98%$

$\frac{\frac{8 !}{3 ! \times 3 ! \times 2 !}}{6 ^{8}} = 0.033%$