If `^n+2C_8:^(n-2)P_4: 57 : 16 ,` find `ndot`

Answer

19

Explanation

We have
`.^(n+2)C_(8): .^(n-2)P_(4)=57: 16`
or `( .^(n+2)C_(8))/(.^(n-2)P_(4))=(57)/(16)`
or `((n+2)!)/(8!(n-6)!)xx((n-6)!)/((n-2)!)=(57)/(16)`
or `(n+2)(n+1)n(n-1)=(57)/(16)xx8!`
`=(19xx3)/(16)xx8xx7xx6xx5xx4xx3xx2xx1`
`implies (n-1)n(n+1)(n+2)=18xx19xx20xx21`
or n-1=18
or n=19