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Find n if ""^(n-1)P(3): ""^(n)P(4) = 1:9...

Find `n` if `""^(n-1)P_(3): ""^(n)P_(4) = 1:9`.

Text Solution

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`.^(n-1)P_(3): .^(n)P_(4) = 1:9`
`rArr 9 xx .^(n-1)P_(3) = 1xx .^(n)P_(4)`
`rArr 9 xx ((n-1)!)/((n-4)!) = (n!)/((n-4)!) xx 1`
`rArr 9 xx (n-1)! = n!`
`rArr 9 xx (n-1)! = n xx (n-1)!`
`rArr n = 9`
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