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Find n, if ""^(n)C(n-4)=5...

Find n, if `""^(n)C_(n-4)=5`

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`implies ""^(n)C_(n)=5`
`implies (n!)/((n-4)!(n-n+4)!)=5`
`implies (n(n-1)(n-2)(n-3)(n-4)!)/((n-4)!4!)=5`
`implies n(n-1)(n-2)(n-3)=5xx4!`
`implies n(n-1)(n-2)(n-3)=5xx4xx3xx2xx1`
`implies n(n-1)(n-2)(n-3)=5(5-1)(5-2)(5-3)`
`therefore n=5`
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