Third-class 8334

If we add one element to set A, the number of third-class variations increases two times. How many elements did the set initially contain?

Correct answer:

n =  5

Step-by-step explanation:

V(n,3) = n(n−1)(n−2) 2⋅ V(n,3) = V(n+1,3) 2⋅ n(n−1)(n−2) = (n+1)n(n−1) 2⋅ (n−2) = (n+1)  2⋅ (n−2)=(n+1)  n=5  n=15​=5  n=5   Verifying Solution:   n1​=n⋅ (n−1)⋅ (n−2)=5⋅ (5−1)⋅ (5−2)=60 n2​=(n+1)⋅ (n)⋅ (n−1)=(5+1)⋅ 5⋅ (5−1)=120  n2​=2n1​

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