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

Explanation

`.^(n+2)C_(8):^(n-2)P_(4) = 57:16`
`(.^(n+2)C_(8))/(.^(n-2)P_(4)) = (57)/(16)`
`rArr ((n+1)!)/(8!(n-6)!).((n-6)!)/((n-2)!) = (57)/(16)`
`rArr ((n+2)(n+1)n(n-1)(n-2)!)/((n-2)!) =(57)/(16) xx 8!`
`rArr (n+2)(n+1)n(n-1)`
`= (57 xx 1 xx 2 xx 3xx 4xx 5xx 6 xx7xx8)/(16)`
`rArr (n+2) (n+1).n(n-1) = 21 xx 20 xx 19 xx 18`
`rArr n = 19` (on comparison).