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If nPr = 5040 and nCr = 210 find n and r.

If nPr = 5040 and nCr = 210 find n and r.

Grade:upto college level

1 Answers

Latika Leekha
askIITians Faculty 165 Points
7 years ago
Given that nPr = 5040 and nCr = 210.
Using their formulas we get,
nPr = 5040 means n! / (n-r)! = 5040 …. (1)
Also, nCr = 210 means n! / r! (n-r)! = 210 …. (2)
Dividing (1) by equation (2), we get
r! = 504/21
= 24
Hence, r = 4.
Another way could be:
nCr = nPr / r!
So, we have 210 = 5040/ r!
This gives r! = 24
Hence r =4.
Thanks & Regards
Latika Leekha
askITIians Faculty

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