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Prove that n(n-1)(n-2) ...(n-r+1)=(n!)/(...

Prove that `n(n-1)(n-2) ...(n-r+1)=(n!)/((n-r)!). `

Text Solution

Verified by Experts

We have
`n(n-1)(n-2) ...(n-r+1)`
` =(n(n-1)(n-2)...(n-r+1).(n-r)!)/((n-r)!) `
[ multiplying num. and denom. by `(n-r)! `]
`=(n!)/((n-r)!). `
Hence, ` n(n-1)(n-2)...(n-r+1)=(n!)/((n-r)!). `
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