यदि `.^(n+2)C_(8):^(n-2)P_(4) = 57 :16`, तो n का मान ज्ञात कीजिए ।

Explanation

`.^(n+2)C_(8) : ^(n-2)P_(4) = 57 : 16`
` rArr (.^(n+2)C_(8))/(.^(n-2)P_(4)) = 57/16`
` rArr ((n+2)!)/(8!(n-6)!) *((n-6)!)/((n-2)!) = 57/16`
` rArr ((n+2)(n+1)*(n-1)(n-2)!)/((n-2)!) = 57/16 xx 8!`
` rArr (n+2)(n+1)n(n-1)`
` = (57xx1xx2xx3xx4xx5xx6xx7xx8)/16`
` rArr (n+2)(n+1)n(n-1)= 21 xx 20 xx 19 xx 18 `
` rArr n = 19` (तुलना करने पर )