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If .^(n+5)P(n+1)=(11(n-1))/2 .^(n+3)Pn ,...

If `.^(n+5)P_(n+1)=(11(n-1))/2 .^(n+3)P_n` , find `n`

Text Solution

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We have, `.^(n+5)C_(n+1)=(11(n-1))/(2)xx.^(n+3)P_(n)`
`implies((n+5)!)/(4!)=(11(n-1))/(2)xx((n+3)!)/(3!)`
`implies((n+5)(n+4))/(4)=(11(n-1))/(2)`
`impliesn^(2)-13n+42=0implies(n-6)(n-7)=0`
`impliesn=6` or n=7
The number of points of intersection of lines is `.^(6)C_(2)` or `.^(7)C`
`=15` or 21
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