Question

Комбинаторика,Вычислите

Answer 1

$displaystyle C_{8}^{5}:P_{3}= frac{8!}{5!(8-5)!}:3!= frac{6*7*8}{6*6}= frac{56}{6}=9 frac{1}{3} \ \ A_{10}^{8}:P_{4}= frac{10!}{(10-8)!}:4!= frac{3*4*5*6*7*8*9*10}{2*3*4}=75600$

Answer 2

C(5, 8) : P(3) = C(3, 8) : P(3) = 8*7*6/(3!*3!) = 8*7*6/(6*6) = 56/6 = 28/3
A(8, 10) : P(4) = 10*9*8*7*6*5*4*3/(1*2*3*4) = 10*9*4*7*6*5 = 75600