C^K/E=C^K/E-1+C^K-1/E-1
решить

Cₐᵇ = a!/(a-b)!b!

n! = 1*2*3**n

n ! = (n - 1)! * n

(n - 1)!/(n-1-k)!k! + (n - 1)!/(n - 1 - (k - 1))! (k - 1)! = (n-1)!*(1/(n-k - 1)!k! + 1/(n - k)!(k -1)!) = (n-1)!*( (n - k)/(n-k)!k! + k/(n-k)!k!) = (n-1)!*n/(n-k)!k! = n!/(n-k)!k! доказано