Sa se calculeze C(4,0) - C(4,1) + C(4, 2) - C(4, 3) + C(4, 4)

Sa se calculeze C(4,0) - C(4,1) + C(4, 2) - C(4, 3) + C(4, 4)

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Se aplica formula combinarilor: combinari de n luate cate k respectiv:

C(n, k) = n! / (k! * (n - k)!)

Pentru a calcula C(4,0) - C(4,1) + C(4,2) - C(4,3) + C(4,4), vom folosi aceasta formula pentru fiecare coeficient binomial:



C(4,0) = 4! / (0! * (4 - 0)!) = 1 

C(4,1) = 4! / (1! * (4 - 1)!) = 4 

C(4,2) = 4! / (2! * (4 - 2)!) = 6 

C(4,3) = 4! / (3! * (4 - 3)!) = 4 

C(4,4) = 4! / (4! * (4 - 4)!) = 1

Inlocuind in expresia initiala, obtinem:

C(4,0) - C(4,1) + C(4,2) - C(4,3) + C(4,4) = 1 - 4 + 6 - 4 + 1 = 0



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