Permutations 6450

Seven times the permutations of n elements equal one-eighth of the permutations of n + 2 elements. What is the number of elements?

Correct answer:

n =  6

Step-by-step explanation:

=(n+2) / =(n+2)(n+1)n /  8⋅ 7=(n+2)(n+1)  8⋅ 7=(n+2)(n+1) −n2−3n+54=0 n2+3n−54=0  a=1;b=3;c=−54 D=b2−4ac=32−4⋅1⋅(−54)=225 D>0  n1,2​=2a−b±D​​=2−3±225​​ n1,2​=2−3±15​ n1,2​=−1.5±7.5 n1​=6 n2​=−9  n>0 n=n1​=6

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