Set variation increase

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?

Final 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   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​

Try another example


Did you find an error or inaccuracy? Feel free to send us. Thank you!







Tips for related online calculators
Are you looking for help with calculating roots of a quadratic equation?
See also our variations calculator.
Do you have a linear equation or system of equations and are looking for its solution? Or do you have a quadratic equation?
Would you like to compute the count of combinations?

You need to know the following knowledge to solve this word math problem:

combinatoricsalgebrabasic operations and conceptsGrade of the word problem

Related math problems and questions: