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Question
If nPr = 1680 and nCr = 70, find n and r.
Solution
nPr = 1680, nCr = 70, n = ? p = ?
nCr = `1/(r!)` nPr
`70/1680 = 1/(r_!)`
`1/24 = 1/(r_i)`
r! = 24
r! = 4 × 3 × 2 × 1
r! = 4!
r = 4
nPr = 1680
`(n!)/(n - 4) = 1680`
`(n (n - 1)(n - 2) (n - 3) (n - 4)!)/(n - 4!) = 1680`
n (n - 1) (n - 2) (n - 3) = 1680
n = 8, 8 (8 - 1) (8 - 2) (8 - 3) = 1680
n = 8, r = 4
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